Answer:
(a) the particle position = 135 m
(b) the velocity of the particle = 44 m/s
(c) the acceleration of the particle = 50 m/s²
Explanation:
Solution to Question 2.
Given;
velocity of a particle, v = 2 - 4t + 2t³
initial position at t = 0, s₀ = 3 m
(a) the particle position at t = 3 s
s = vt
s = (2 - 4t + 2t³)t
s = 2t - 4t² + 2t⁴
s = s₀ + s₃
s = s₀ + 2(3) - 4(3²) + 2(3⁴)
s = s₀ + 6 - 36 + 162
s = s₀ + 132 m
s = 3m + 132 m
s = 135 m
(b) the velocity of the particle at t = 3 s
v = 2 - 4t + 2t³ = 2 - 4(3) + 2(3)³
v = 44 m/s
(c) the acceleration of the particle at t = 3s
v = 2 - 4t + 2t³
[tex]a = \frac{dv}{dt} \\\\a = \frac{d}{dt} (2 -4t + 2t^3)\\\\a = -4 + 6t^2[/tex]
a = -4 + 6(3)²
a = 50 m/s²
A 2000 kg car moving at 100 km/h crosses the top of a hill with a radius of curvature of 100 m. What is the normal force exerted by the seat on the driver if the mass of the driver is 60 kg?
Answer:
The normal force the seat exerted on the driver is 125 N.
Explanation:
Given;
mass of the car, m = 2000 kg
speed of the car, u = 100 km/h = 27.78 m/s
radius of curvature of the hill, r = 100 m
mass of the driver, = 60 kg
The centripetal force of the driver at top of the hill is given as;
[tex]F_c = F_g - F_N[/tex]
where;
Fc is the centripetal force
[tex]F_g[/tex] is downward force due to weight of the driver
[tex]F_N[/tex] is upward or normal force on the drive
[tex]F_N = F_g-F_c\\\\F_N = mg - \frac{mv^2}{r} \\\\F_N = (60 \times 9.8) -\frac{60 \ \times \ 27.78^2 \ }{100} \\\\F_N = 588 \ N - 463 \ N\\\\F_N = 125 \ N[/tex]
Therefore, the normal force the seat exerted on the driver is 125 N.
The normal force exerted by the seat on the driver if the mass of the driver is 60 kg is of 125 N.
Given data:
The mass of car is, m' = 2000 kg.
The speed of car is, v = 100 km/h = 100 × 5/18 = 27.77 m/s.
The radius of curvature of path is, r = 100 m.
The mass of driver is, m = 60 kg.
In this case, the normal force on the driver is equal to the difference between weight of the driver and the centripetal force on the driver. Then the expression is given as,
[tex]N'= W - F\\\\N '= mg-\dfrac{mv^{2}}{r}[/tex]
Solving as,
[tex]N' = (60 \times 9.8)-\dfrac{60 \times 27.77^{2}}{100}\\\\N' = 125\;\rm N[/tex]
Thus, we can conclude that the normal force exerted by the seat on the driver if the mass of the driver is 60 kg is of 125 N.
Learn more about the centripetal force here:
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What is the formula to finding your target heart rate.
The cars in a soapbox derby have no engines; they simply coast downhill. Which of the following design criteria is best from a competitive point of view? a. The car's wheels should b. have large moments of inertia be massive c. be hoop-like wheels rather than solid disks d. have small moments of inertia
Complete question is;
The cars in a soapbox derby have no engines; they simply coast downhill. Which of the following design criteria is best from a competitive point of view?
The car's wheels should;
A. have large moments of inertia
B. be massive
C. be hoop-like wheels rather than solid disks
D. have small moments of inertia
Answer:
D. The car's wheels should have small moments of inertia
Explanation:
They are simply cast downhill due to no engine and thus the solid wheels will have very small moments of inertia and will therefore accelerate at a faster rate.
Looking at the options, the correct one that corresponds to the description I just made is Option D.
The car's wheels should have small moments of inertia.
What is Inertia?This is defined as the resistance of any physical object to a change in its velocity.
We told they were cast downhill due to no engine and the solid wheels having very small moments of inertia causing increase in acceleration depicts option D which was why it was chosen.
Read more about Inertia here https://brainly.com/question/1140505
Determine whether each of the following statements is true or false.
a. An object's weight is always equal to its mass.
b. The force of tension always pushes.
c. The magnitude of the sum of the forces on an object is never greater than its weight. Explain.
Answer:
a) For an object with mass M, in a region with a gravitational acceleration g, is:
W = M*g
Then the weight is g times the mass of the object, this means that the weight is not always equal to the mass of the object, this first statement is false.
For example, in Earth the gravitational acceleration is 9.8m/s^2
Then there is no object in Earth with a weight equal to its mass.
b) The force of tension can be the force in a piece of string that is holding an object with mass M.
The force of tension will be always pointing in the direction to the "center" of the string, then it does not push, the tension force "pulls"
The statement is false.
c) we know that the weight is:
W = M*g
This is a force, that for an object that is in the air, will pull the object back to the ground.
Suppose that we also have that object attached to a string, and the object is in the air, now the object starts to fall due to its weight and we also pull down with the string, then the total force pulling down will be the weight plus the tension of the string, then we will have a force larger (in magnitude) than the weight, which means that the statement is false.
Use the image below to answer the following question (ruler not to scale).
If magnet B is moved closer to magnet A, how will magnetic potential energy be affected?
O. It will become zero.
O. It willincrease.
O. It will decrease.
O. It will stay the same.
Please help
Answer:
it depends on wether the + and - are facing eachother
or away from eachother
Explanation:
Answer:
Yes, they are correct, you need to include all parts of the question, don't just copy and paste the words. But in the diagram that was supposed to be there, the magnets' north poles are facing each other. Therefore they would push away from each other if they were to get any closer. So, the magnetic potential energy would decrease due to their movement away from each other. So your answer is (C. It will decrease.
Explanation:
A ball has a mass of 250g. The ball is kicked and this applies a force 15 N to the ball, as shown in the diagram. How much does the ball accelerate by in the direction of the kick?
Answer:
0.06 m/s²
Explanation:
force= mass × acceleration
acceleration= force / mass
acceleration= 15/250= 0.06 m/s²
hope it helps! please mark me brainliest..
Have a good day ahead
The acceleration of the ball in the direction of the kick will be 600 m/[tex]s^{2}[/tex]
We have a Ball.
We have to determine the acceleration of the ball in the direction of the kick.
What is Force?The product of mass and acceleration of a body is called force.
Force = Mass x Acceleration.
According to the question, we have -
Mass = 250 g = 0.025 Kg
Force = 15 N
Then, the acceleration of the ball in the direction of the kick will be -
F = m x a
a = F / m
a = 15 / 0.025 = 600 m/[tex]s^{2}[/tex]
Hence, the acceleration of the ball in the direction of the kick will be 600 m/[tex]s^{2}[/tex]
To solve more questions on Force, visit the link below-
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Answer all these questions correctly and will mark brainliest!
1. In Football a field goal is kicked for how many points?
2. Football a touch down is worth how many points?
3. What part of the body can a goalie in soccer use that no one else can?
4. How many quarters are in a football game?
5. How many players are on the field in football?
6. Who invented basketball?
7. Who invented the game Nukem?
8. In volleyball can a ball (Including serve) be played off of the net?
9. When did basketball become an Olympic sport?
10.How many quarters are in a football game?
Inappropriate answers will be reported
Answer:
1. 3 points
2. 6 points
3. goalkeeper
4. four quarters
5. eleven players
6. James Naismith
7. Duke nukem ( I'm not sure)
8. no
9. 1936
10. four
HOPE IT'S HELP :)
alpha and beta rays origin is same
Answer:
Alpha particles carry a positive charge, beta particles carry a negative charge, and gamma rays are neutral. An alpha particle is made up of two protons and two neutrons bound together. Beta particles are high energy electrons. Gamma rays are waves of electromagnetic energy, or photons.
To travel at a constant speed,a car engine provides 24 KW of useful powers. The driving force on the car is 600N.AT what speed does it travel? A 2.5 B 4.0 C.25 D 40
Answer: D. 40
Explanation:
Power = Force * Velocity
Force = 600N
Power needs to be converted to Watts:
= 24 * 1,000
= 24,000 W
24,000 = 600 * Velocity
Velocity = 24,000/600
= 40 m/s
A child swings a tennis ball attached to a 0.626-m string in a horizontal circle above his head at a rate of 4.50 rev/s.
a. What is the centripetal acceleration of the tennis ball?
b. The child now increases the length of the string to 1.00m but has to decrease the rate of rotation to 4.00 rev/s. Is the speed of the ball greater now or when the string was shorter?
c. What is the centripetal accleration of the tennis ball when the string is 1.00 m in length?
Explanation:
Length of a string, l = 0.626 m
A tennis ball revolves in a horizontal circle above his head at a rate of 4.50 rev/s.
(a) The centripetal acceleration of the tennis ball is given by :
[tex]a=\omega^2r\\\\a=(4.5\times 2\pi)^2\times 0.626\\\\=500.44\ m/s^2[/tex]
(b) When r = 0.626 m and ω = 4.50 rev/s
Speed,
[tex]v=r\omega\\\\=0.626\times 4.50 \times 2\pi\\\\=17.69\ m/s[/tex]
When r = 1 m and ω = 4 rev/s
Speed,
[tex]v=r\omega\\\\=1\times 4 \times 2\pi\\\\=25.13\ m/s[/tex]
Speed is more in second case when child now increases the length of the string to 1.00m but has to decrease the rate of rotation to 4.00 rev/s.
(c) [tex]a=\omega^2r\\\\a=(4\times 2\pi)^2\times 1\\\\=631.65\ m/s^2[/tex]
Hence, this is the required solution.
My dad gifted me a calculator. I have observed that very small cells are used in a calculator. What are these cells called and what are their main advantage?
What is the average reaction time of people
Answer:
the average reaction time is 0.25 seconds.
The two sleds shown below are about to collide. If they stick together in the collision, what will happen after the collision? (In this collision, there is no friction
between the sleds and the snow.)
A. The two sleds will move to the left.
O B. The two sleds will move to the right
O C. The two sleds will be motionless in the middle.
O D. There is not enough information to know which sled will be pushed backward,
om
Answer:
B. The two sleds will move to the right.
Explanation:
I majored in physics
Answer:
b
Explanation:
a fisherman moves from one end of a boat to another
Answer:
That isnt a question so no one will know the answer to what you are talking about. I suggest adding a sceenshot or picture of the question.
In the graph, which two regions show the particle undergoing zero acceleration and negative acceleration respectively?
A. BC shows zero acceleration, and AB shows negative acceleration.
B. AB shows zero acceleration, and CD shows negative acceleration.
C. BC shows zero acceleration, and CD shows negative acceleration.
D. AB shows zero acceleration, and BC shows negative acceleration.
Answer:
Option C. BC shows zero acceleration, and CD shows negative acceleration.
Explanation:
To successfully answer the question given above, we must know the meaning of zero acceleration and negative acceleration respectively.
Zero acceleration simply means the object is not accelerating. This implies that velocity of the object is constant (i.e unchanged) with time.
Negative acceleration simply means the object is decelerating i.e coming to rest.
Now, let us answer the question given above.
From the question given above, the following data were obtained:
1. AB indicates that the particle is accelerating because the velocity increased from A to B with time.
2. BC indicates zero acceleration because the velocity of the Particle is constant (i.e unchanged) with time.
3. CD indicates that the object is coming to rest i.e decelerating (negative acceleration) because the velocity of the object decreased from C to D with time.
From the above illustrations, we can see that only option C gives the correct answer to the question.
Answer:
Option C. BC shows zero acceleration, and CD shows negative acceleration.
Explanation:
*WILL MARK BRAINLIEST*
A glass window (n = 1.52) has a
uniform layer of ice on it (n = 1.31).
What is the critical angle for a ray
trying to pass from glass to ice?
(Water n = 1.33, Air n = 1.00)
(Unit = deg)
Answer:
1.52
Explanation:
Answer: 59.5 deg
Explanation:
I got it right on acellus ✅
Question 12 of 15
The following equation is an example of
decay
Answer:
beta decay
Explanation:
the decay above is known as beta decay because give electron after it decay.
Answer: It’s definitely “Beta” friend!
Tell me the max amount you should owe on this card.
Your credit limit is $1,000.
What is the max you should ever owe on this card?
$
Your credit limit is $2,500.
What is the max you should ever owe on this card?
$
Answer:
the max is 2,500 or less
Explanation:
because you cant owe anymore
I’m in a test and I’m sort of being timed here’s a photo of question
Answer: D.
Explanation:
Answer:
i think the answer is b
Explanation:
playing sports often require both
Remaining Time: 1 hour, 49 minutes, 34 seconds.
Question Completion Status:
QUESTION 8
If the magnification is calculated to be +0.5 in a particular situation, what does that tell you about the image?
O A. It is bigger by 0.5
OB
It is half the size of the object.
O C. It is twice the size of the object.
O D. It is smaller by 0.5
O E. It tells you nothing about the image.
QUESTION 9
Explanation:
i think C . it is twice the size of the object
A tennis player tosses a tennis ball straight up and then catches it after 1.25 s at the same height as the point of release.
a. What is the acceleration of the ball while it is in flight?
b. What is the velocity of the ball when it reaches its maximum height?
c. Find the initial velocity of the ball.
d. Find the maximum height it reaches.
Answer:
A. 9.8 m/s²
B. Zero
C. 6.125 m/s
D. 1.91 m
Explanation:
From the question given above, the following data were obtained:
Time (T) spent in the air = 1.25 s
A. Determination of the acceleration of the ball.
From the description given in question above, the motion of the tennis ball is motion under gravity. Hence, the ball will experience an acceleration due to gravity of 9.8 m/s²
B. Determination of the velocity at maximum height.
Maximum height is the greatest point reached by the tennis ball above the ground. At maximum height, the velocity of the tennis ball is zero since it has no further force to propel it upward.
C. Determination of the initial velocity of the ball.
We'll begin by calculating the time taken to reach the maximum height. This can be obtained as follow:
Time (T) spent in the air = 1.25 s
Time (t) to reach the maximum height =?
T = 2t
1.25 = 2t
Divide both side by 2
t = 1.25 / 2
t = 0.625 s
Finally, we shall determine the initial velocity of the ball. This can be obtained as follow:
Time (t) to reach the maximum height = 0.625 s
Acceleration due to gravity (g) = 9.8 m/s²
Final velocity (v) = 0 (at maximum height)
Initial velocity (u) =?
v = u – gt (since the ball is going against gravity)
0 = u – (9.8 × 0.625)
0 = u – 6.125
Collect like terms
0 + 6.125 = u
u = 6.125 m/s
Thus, the initial velocity of the ball is 6.125 m/s
D. Determination of the maximum height.
Acceleration due to gravity (g) = 9.8 m/s²
Final velocity (v) = 0 (at maximum height)
Initial velocity (u) = 6.125 m/s
Maximum height (h) =?
v² = u² – 2gh (since the ball is going against gravity)
0² = 6.125² – (2 × 9.8 × h)
0 = 37.52 – 19.6h
Collect like terms
0 – 37.52 = – 19.6h
– 37.52 = – 19.6h
Divide both side by – 19.6
h = – 37.52 / – 19.6
h = 1.91 m
Thus, the maximum height reached by the ball is 1.91 m
convert 144 km/h to m/s
Answer:
40m/s
Explanation:
144km/h
1km=1000m
1hr=3600secs
144×1000/3600=
40m/s
Is the amount of stretch of the springs proportional to the hanging mass? Explain briefly.
Derive a theoretical expression to find k-equivalent for springs in parallel and springs in series.
Answer:
When connected in parallel, the extension of both springs is the same, and the total elastic force will be equal to the sum of the forces in each spring: x=x1=x2,F=F1+F2. F=F1+F2,⇒kx=k1x1+k2x2=(k1+k2)x,⇒k=k1+k2.
Yes. The amount of stretch of a spring is proportional to the hanging mass.
According to Hooke's Law, the restoring force of the spring F is:
F = -kx
k is the spring constant and x is the stretch of spring.
The restoring force F is in opposite direction of the weight of the hanging mass which is mg
⇒ F = -mg
mg = -kx
x = mg/k
Hence x, the stretch of the spring is directly proportional to the hanging mass.
(i) If two springs are connected in parallel, their k- equialent is
[tex]k= k_{1}+k_{2}[/tex]
(ii) If two springs are connected in series, their k- equialent is
[tex]\frac{1}{k}=\frac{1}{k_{1} } +\frac{1}{k_{2} }[/tex]
Learn more about Hooke's Law:
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Dee Liverance shoots an arrow out of her bow. The string is stretched 57 cm, and when
released the arrow leaves the bow in 0.17 s. What is the acceleration of the arrow?
Answer:
Mr. Dececco will not be happy
Explanation:
I'll give you a hint, the answer starts with the number 3. Use the kinematics equation of [tex]delta\ x =v_{0}t+ \frac{1}{2}at^{2}[/tex]
An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V. What must be the ratio of the number of turns in the secondary to the number of turns in the primary
Answer:
[tex]N_s : N_p = 20 : 1[/tex]
Explanation:
From the question we are told that
The primary voltage is [tex]V_p = 120 \ V[/tex]
The secondary voltage is [tex]V_s = 6 \ V[/tex]
Generally from the transformer equation we have that
[tex]\frac{V_p}{V_s} = \frac{N_p}{N_s}[/tex]
So
[tex]\frac{120}{6} = \frac{N_p}{N_s}[/tex]
=> [tex]\frac{N_p}{N_s} = 20[/tex]
Therefore the ratio of the number of turns in the secondary to the number of turns in the primary is
[tex]N_s : N_p = 20 : 1[/tex]
7. A beam of light converges at a point P. Now a lens is placed in the path of the convergent
beam 12cm from P. At what point does the beam converges if the lens is a) a convex lens of
focal length 20cm and b) a concave lens of focal length 16cm.
Answer:
Lens at a distance = 7.5 cm
Lens at a distance = 6.86 cm (Approx)
Explanation:
Given:
Object distance u = 12 cm
a) Focal length = 20 cm
b) Focal length = 16 cm
Computation:
a. 1/v = 1/u + 1/f
1/v = 1/20 + 1/12
v = 7.5 cm
Lens at a distance = 7.5 cm
b. 1/v = 1/u + 1/f
1/v = 1/16 + 1/12
v = 6.86 cm (Approx)
Lens at a distance = 6.86 cm (Approx)
1. The center of gravity of both cats and humans is roughly in the thoracic region. However, they each bear their weight very differently. a. Which are the major, weight-bearing structures of the two skeletons
Answer:
Major, weight-bearing structures are the bones of the body that are strong and dense to be able to bear the weight of the body. The major, weight-bearing structures of cat and human skeletons are :
Human skeleton: The body weight of an individual is on his pelvic girdles that are attached to the bones of lower limbs. Thigh bones, leg bones, and bones of feet comprise lower limbs The lower limbs consist of the thigh, the leg, and the foot.
Cat skeleton: cats are quadrupedal so it bears all the body weight on shoulders and legs that includes the Scapula and pelvis.
When a cold air mass catches up with a warm air mass, the resut is often
a(n)
front.
Answer:
a cold front i think
Explanation:
A horizontal force of 150 N is used to push a 38.0 kg packing crate a distance of 6.85 m on a rough horizontal surface. If the crate moves at constant speed, find each of the following.
a) find the work done by the 150N force:
b) find the coefficient of kinetic energy between the crate and rough surface
Answer:
0.40
Explanation:
a) Work done is expressed as
W = Force × distance
Given.
Force = 150N
Distance = 6.85m
Workdone = 150×6.85
Work done = 1027.5Joules
b) According to Newton's second law
\sumFx = ma
Fm - Ff = ma
Since speed is constant, acceleration us zero
Fm - Ff = 0
Fm = Ff = nR
Fm is the moving force
Ff is the frictional force
n is the coefficient of kinetic energy between the crate and rough surface
R is the reaction
From the formula;
Fm = nR
n = Fm/R
n = Fm/mg
n = 150/38(9.8)
n = 150/372.4
n = 0.40
Hence the coefficient of kinetic energy between the crate and rough surface is 0.40
Two particles, an electron and a proton, move in a circular path in a uniform magnetic field of intensity B=1.23 T. Find the ratio between the time period of the proton Tp to the electron Te (i.e., find 'p)
Answer:
The ratio of the time period of the proton to the electron is 1835.16.
Explanation:
Given that,
Two particles, an electron and a proton, move in a circular path in a uniform magnetic field of intensity B=1.23 T
We need to find the ratio between the time period of the proton Tp to the electron Te.
The time period in magnetic field is given by :
[tex]T=\dfrac{2\pi m}{qB}[/tex]
For proton, time period is :
[tex]T_P=\dfrac{2\pi m_P}{q_pB}\ ....(1)[/tex]
For an electron, the time period is :
[tex]T_e=\dfrac{2\pi m_e}{q_eB}\ ....(2)[/tex]
From equation (1) and (2) :
[tex]\dfrac{T_p}{T_e}=\dfrac{\dfrac{2\pi m_p}{q_pB}}{\dfrac{2\pi m_e}{q_eB}}\\\\As\ q_e=q_p\\\\\dfrac{T_p}{T_e}=\dfrac{m_p}{m_e}\\\\=\dfrac{1.67\times 10^{-27}}{9.1\times 10^{-31}}\\\\=1835.16[/tex]
So, the ratio of the time period of the proton to the electron is 1835.16.