Question 1

Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/ $\mathrm { s } ^ { 2 }$ . How long after car A begins to accelerate does it take car A to overtake car B?
A)5.50 s
B)12.6 s
C)19.0 s
D)316 s
E)Car A never overtakes car B.

Accepted Answer

To find the time it takes for car A to overtake car B, we set the distance traveled by both cars equal to each other. Using the equations of motion, for car A: $d_A = 22t + 0.5 \times 2.4 \times t^2$ and for car B: $d_B = 29t + 300$. Setting $d_A = d_B$ and solving for $t$, we find $t \approx 19.0$ seconds.

Question 2

A train starts from rest and accelerates uniformly until it has traveled 5.6 km and acquired a forward velocity of $42 \mathrm {~m} / \mathrm { s }$ The train then moves at a constant velocity of $42 \mathrm {~m} / \mathrm { s }$ for 420 s. The train then slows down uniformly at $0.065 \mathrm {~m} / \mathrm { s } ^ { 2 }$ until it is brought to a halt. The acceleration during the first 5.6 km of travel is closest to which of the following?
A)0.16 m/ $\mathrm { s } ^ { 2 }$
B)0.14 m/ $\mathrm { s } ^ { 2 }$
C)0.17 m/ $\mathrm { s } ^ { 2 }$
D)0.19 m/ $\mathrm { s } ^ { 2 }$
E)0.20 m/ $\mathrm { s } ^ { 2 }$

Accepted Answer

Using the equation $v^2 = u^2 + 2as$, where $v = 42 \, \mathrm{m/s}$, $u = 0$, and $s = 5600 \, \mathrm{m}$, we solve for $a$ to find $a \approx 0.16 \, \mathrm{m/s^2}$.

Question 3

An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s² and there is no atmosphere. How long does it take for the instrument to return to where it was thrown? A)6.0 s B)8.0 s C)10 s D)12 s

Accepted Answer

The answer of An instrument is thrown upward with a...

Question 4

A train starts from rest and accelerates uniformly until it has traveled 2.1 km and acquired a forward velocity of $24 \mathrm {~m} / \mathrm { s }$ The train then moves at a constant velocity of $24 \mathrm {~m} / \mathrm { s }$ for 400 s. The train then slows down uniformly at $0.065 \mathrm {~m} / \mathrm { s } ^ { 2 }$ until it is brought to a halt. The distance traveled by the train while slowing down is closest to
A)4.4 km.
B)4.2 km.
C)4.0 km.
D)3.8 km.
E)3.6 km.

Accepted Answer

The distance traveled while slowing down can be calculated using the formula $ v^2 = u^2 + 2as $, where $ v = 0 $, $ u = 24 \, \text{m/s} $, and $ a = -0.065 \, \text{m/s}^2 $. Solving for $ s $ gives approximately 4.4 km.

Question 5

A car is traveling with a constant speed when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration of magnitude 3.50 m/s². If the car comes to a stop in a distance of 30.0 m, what was the car's original speed? A)10.2 m/s B)14.5 m/s C)105 m/s D)210 m/s E)315 m/s

Accepted Answer

We can use the kinematic equation, $v_f^2 = v_i^2 + 2a\Delta x$, where $v_f$ is final velocity (zero in this case), $v_i$ is initial velocity (what we're solving for), $a$ is acceleration (-3.50 m/s$^2$), and $\Delta x$ is distance (-30.0 m). Plugging in the values and solving for $v_i$, we get:
$0^2 = v_i^2 + 2(-3.50)(-30.0)$
$v_i^2 = 210$
$v_i = \sqrt{210} \approx 14.5$ m/s
Therefore, the answer is B.

Question 6

A car is moving with a constant acceleration. At time t = 5.0 s its velocity is 8.0 m/s in the forward direction, and at time t = 8.0 s its velocity is 12.0 m/s forward. What is the distance traveled in that interval of time?
A)10 m
B)20 m
C)30 m
D)40 m
E)50 m

Accepted Answer

We use the equation:

d = (vf + vi)/2 * t

where
vf = final velocity = 12.0 m/s
vi = initial velocity = 8.0 m/s
t = time interval = 8.0 s - 5.0 s = 3.0 s

Plugging in the values, we get:

d = (12.0 m/s + 8.0 m/s)/2 * 3.0 s
d = 10.0 m/s * 3.0 s
d = 30 m

Therefore, the distance traveled in that interval of time is 30 m. The best choice is (C).

Question 7

A car starts from rest and accelerates at a steady 6.00 m/s². How far does it travel in the first 3.00 s? A)9.00 m B)18.0 m C)27.0 m D)36.0 m E)54.0 m

Accepted Answer

We can use the kinematic equation:

d = 1/2 at^2

where d is the distance traveled, a is the acceleration, and t is the time.

Plugging in a = 6.00 m/s^2 and t = 3.00 s, we get:

d = 1/2 (6.00 m/s^2) (3.00 s)^2 = 27.0 m

Therefore, the car travels 27.0 m in the first 3.00 s. The correct answer is (C).

Question 8

A stone is thrown with an initial upward velocity of 7.0 m/s and experiences negligible air resistance. If we take upward as the positive direction, what is the velocity of the stone after 0.50 s?
A)2.1 m/s
B)4.9 m/s
C)-2.1 m/s
D)-4.9 m/s
E)0.00 m/s

Accepted Answer

Using the kinematic equation for velocity:

vf = vi + at

Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time

Since we are taking upward as the positive direction, acceleration due to gravity will be negative (-9.8 m/s^2) because it is acting in the opposite direction of the initial velocity. Therefore:

vf = vi + at
vf = 7.0 m/s + (-9.8 m/s^2)(0.50 s)
vf = 7.0 m/s - 4.9 m/s
vf = 2.1 m/s

The final velocity after 0.5 seconds is 2.1 m/s upward (or positive). Therefore, the correct choice is A).

Question 9

A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s² and there is no atmosphere. What is the maximum height reached by the laser? A)8.0 m B)18 m C)48 m D)144 m

Accepted Answer

Using the formula:
Final velocity (v)² = initial velocity (u)² + 2as
where
v = 0 m/s (at maximum height, the velocity becomes zero)
u = 12 m/s (initial velocity)
a = 1.5 m/s² (acceleration due to gravity)
s = maximum height reached by the laser

0 = 12² - 2(1.5)s
0 = 144 - 3s
3s = 144
s = 48 m

Therefore, the maximum height reached by the laser is 48 m.

Question 10

An airplane starts from rest and accelerates at a constant 10.8 m/s². What is its speed at the end of a 400 m-long runway? A)37.0 m/s B)93.0 m/s C)65.7 m/s D)4320 m/s E)186 m/s

Accepted Answer

The answer of An airplane starts from rest and accelerates...

Question 11

Acceleration is sometimes expressed in multiples of g, where $g = 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ is the acceleration of an object due to the earth's gravity. In a car crash, the car's forward velocity may go from $29 \mathrm {~m} / \mathrm { s }$ to $0 \mathrm {~m} / \mathrm { s }$ in $0.15 \mathrm {~s}$ How many g's are experienced, on average, by the driver?
A)20 g
B)14 g
C)24 g
D)26 g

Accepted Answer

The average acceleration is calculated using the formula $ a = \frac{\Delta v}{\Delta t} = \frac{29 \, \mathrm{m/s}}{0.15 \, \mathrm{s}} = 193.33 \, \mathrm{m/s^2} $. To express this in terms of g, divide by $9.8 \, \mathrm{m/s^2}$: $ \frac{193.33}{9.8} \approx 19.73 $, which rounds to 20 g.

Question 12

A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the brakes, causing the car to slow down with a uniform acceleration of magnitude 3.50 m/s². How far does the car travel after the driver put on the brakes until it comes to a stop? A)4.57 m B)9.14 m C)112 m D)146 m E)292 m

Accepted Answer

The answer of A car is moving with a speed...

Question 13

A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s² and there is no atmosphere. What is the speed of the hammer after 8.0 s? A)7.0 m/s B)14 m/s C)21 m/s D)64 m/s

Accepted Answer

The answer of A hammer is thrown upward with a...

Question 14

An astronaut on a strange new planet having no atmosphere finds that she can jump up to a maximum height of 27 m when her initial upward speed is 6.0 m/s. What is the magnitude of the acceleration due to gravity on the planet?

Accepted Answer

The answer of An astronaut on a strange new planet...

Question 15

A car is traveling with a constant speed of 30.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration. The car comes to a stop in a distance of 120 m. What was the acceleration of the car as it slowed down? A)3.75 m/s² B)4.00 m/s² C)4.25 m/s² D)4.50 m/s² E)4.75 m/s²

Accepted Answer

The acceleration can be found using the equation $v^2 = u^2 + 2as$, where $v = 0$ (final velocity), $u = 30.0$ m/s (initial velocity), $s = 120$ m (distance), and $a$ is the acceleration. Rearranging for $a$, we get $a = -\frac{u^2}{2s}$. Substituting the given values, $a = -\frac{(30.0)^2}{2 \times 120} = -\frac{900}{240} = -3.75$ m/s$^2$. The negative sign indicates deceleration.

Question 16

A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds the ball has rolled 91 m with constant acceleration, and 1.0 s later it reaches the bottom of the incline.
(a)What was the ball's acceleration?
(b)How long was the incline?

Accepted Answer

The answer of A soccer ball is released from rest...

Question 17

A baseball is hit with a bat and, as a result, its direction is completely reversed and its speed is doubled. If the actual contact with the bat lasts 0.45 s, what is the ratio of the magnitude of the average acceleration of the ball to its original speed? A)6.7 s^-¹ B)4.4 s^-1 C)2.2 s^-1 D)0.15 s^-1

Accepted Answer

The answer of A baseball is hit with a bat...

Question 18

Assuming equal rates of uniform acceleration in both cases, how much further would you travel if braking from $56 \mathrm { mi } / \mathrm { h }$ to rest than from $28 \mathrm { mi } / \mathrm { h }$ ?
A)4 times farther
B)3.2 times farther
C)4.8 times farther
D)5.2 times farther

Accepted Answer

The stopping distance is proportional to the square of the initial speed. Therefore, if the speed is doubled from 28 mi/h to 56 mi/h, the stopping distance becomes $ (56/28)^2 = 4 $ times farther.

Question 19

A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s² and there is no atmosphere. How long does it take for the laser to reach the maximum height? A)8.0 s B)11 s C)14 s D)16 s

Accepted Answer

The time taken for an object to reach maximum height can be calculated using the formula t = v/g, where v is the initial velocity and g is the acceleration due to gravity. 
So, t = 12/1.5 = 8.0 seconds. Therefore the answer is A.

Question 20

A car is traveling at 26.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with constant acceleration. The car comes to a stop in a distance of 120 m. How fast was the car moving when it was 60.0 m past the point where the brakes were applied?
A)22.5 m/s
B)18.4 m/s
C)15.0 m/s
D)12.1 m/s
E)9.20 m/s

Accepted Answer

We can solve this problem using the kinematic equation:

v^2 = u^2 + 2as

Where: 
v = final velocity (0 m/s) 
u = initial velocity 
a = acceleration 
s = displacement (120 m)

We can rearrange this equation to solve for u:

u = sqrt(v^2 - 2as)

u = sqrt((26.0 m/s)^2 - 2(−a)(120 m))

We know that the acceleration is negative because the car is slowing down:

a = - v^2 / 2s
a = - (26.0 m/s)^2 / (2 x 120 m)

a = -11.05 m/s^2

Substituting this value into the previous equation:

u = sqrt((26.0 m/s)^2 - 2(-11.05 m/s^2)(120 m))

u = 18.4 m/s

Therefore, the car was traveling at 18.4 m/s when it was 60.0 m past the point where the brakes were applied. The answer is B.

Quiz 2: Motion in One Dimension

Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/ s2\mathrm { s } ^ { 2 }s2 . How long after car A begins to accelerate does it take car A to overtake car B?

An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s2 and there is no atmosphere. How long does it take for the instrument to return to where it was thrown?

A car is traveling with a constant speed when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration of magnitude 3.50 m/s2. If the car comes to a stop in a distance of 30.0 m, what was the car's original speed?

A car is moving with a constant acceleration. At time t = 5.0 s its velocity is 8.0 m/s in the forward direction, and at time t = 8.0 s its velocity is 12.0 m/s forward. What is the distance traveled in that interval of time?

A car starts from rest and accelerates at a steady 6.00 m/s2. How far does it travel in the first 3.00 s?

A stone is thrown with an initial upward velocity of 7.0 m/s and experiences negligible air resistance. If we take upward as the positive direction, what is the velocity of the stone after 0.50 s?

A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. What is the maximum height reached by the laser?

An airplane starts from rest and accelerates at a constant 10.8 m/s2. What is its speed at the end of a 400 m-long runway?

A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the brakes, causing the car to slow down with a uniform acceleration of magnitude 3.50 m/s2. How far does the car travel after the driver put on the brakes until it comes to a stop?

A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s2 and there is no atmosphere. What is the speed of the hammer after 8.0 s?

An astronaut on a strange new planet having no atmosphere finds that she can jump up to a maximum height of 27 m when her initial upward speed is 6.0 m/s. What is the magnitude of the acceleration due to gravity on the planet?

A car is traveling with a constant speed of 30.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration. The car comes to a stop in a distance of 120 m. What was the acceleration of the car as it slowed down?

A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds the ball has rolled 91 m with constant acceleration, and 1.0 s later it reaches the bottom of the incline. (a)What was the ball's acceleration? (b)How long was the incline?

A baseball is hit with a bat and, as a result, its direction is completely reversed and its speed is doubled. If the actual contact with the bat lasts 0.45 s, what is the ratio of the magnitude of the average acceleration of the ball to its original speed?

Assuming equal rates of uniform acceleration in both cases, how much further would you travel if braking from 56mi/h56 \mathrm { mi } / \mathrm { h }56mi/h to rest than from 28mi/h28 \mathrm { mi } / \mathrm { h }28mi/h ?

A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. How long does it take for the laser to reach the maximum height?

A car is traveling at 26.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with constant acceleration. The car comes to a stop in a distance of 120 m. How fast was the car moving when it was 60.0 m past the point where the brakes were applied?

Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/ $\mathrm { s } ^ { 2 }$ . How long after car A begins to accelerate does it take car A to overtake car B?

An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s² and there is no atmosphere. How long does it take for the instrument to return to where it was thrown?

A car is traveling with a constant speed when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration of magnitude 3.50 m/s². If the car comes to a stop in a distance of 30.0 m, what was the car's original speed?

A car starts from rest and accelerates at a steady 6.00 m/s². How far does it travel in the first 3.00 s?

A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s² and there is no atmosphere. What is the maximum height reached by the laser?

An airplane starts from rest and accelerates at a constant 10.8 m/s². What is its speed at the end of a 400 m-long runway?

A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the brakes, causing the car to slow down with a uniform acceleration of magnitude 3.50 m/s². How far does the car travel after the driver put on the brakes until it comes to a stop?

A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s² and there is no atmosphere. What is the speed of the hammer after 8.0 s?

Assuming equal rates of uniform acceleration in both cases, how much further would you travel if braking from $56 \mathrm { mi } / \mathrm { h }$ to rest than from $28 \mathrm { mi } / \mathrm { h }$ ?

A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s² and there is no atmosphere. How long does it take for the laser to reach the maximum height?