Question 1

A cheetah can run at approximately 100 km/hr and a gazelle at 80.0 km/hr.If both animals are running at full speed,with the gazelle 60.0 m ahead,how long before the cheetah catches its prey?
A) 6.30 s
B) 21.6 s
C) 5.40 s
D) 10.8 s

Accepted Answer

D

Question 2

A cheetah can maintain its maximum speed of 100 km/hr for 35.0 seconds.What minimum distance must a gazelle running 80.0 km/hr be ahead of the cheetah to escape?
A) 194 m
B) 167 m
C) 70.0 m
D) 125 m

Accepted Answer

Explanation:The cheetah runs 100 km/hr for 35.0 s, so it covers a distance of:$$d_c = (100 \frac{km}{hr})(\frac{35.0 s}{3600 s/hr}) = 0.972 km = 972 m$$The gazelle runs 80.0 km/hr, so it covers a distance of:$$d_g = (80.0 \frac{km}{hr})(\frac{35.0 s}{3600 s/hr}) = 0.741 km = 741 m$$Therefore, the gazelle must be ahead of the cheetah by a minimum distance of:$$d = d_c - d_g = 972 m - 741 m = 194 m$$

Question 3

Rita accelerates a 0.40-kg ball from rest to 12 m/s during the 0.15 s in which her foot is in contact with the ball.What average force does she apply to the ball during the kick?
A) 48 N
B) 32 N
C) 24 N
D) 64 N

Accepted Answer

B

Question 4

When a drag strip vehicle reaches a velocity of 60 m/s,it begins a negative acceleration by releasing a drag chute and applying its brakes.While reducing its velocity back to zero,its acceleration along a straight line path is a constant −6.0 m/s².What displacement does it undergo during this deceleration period? A) 120 m B) 300 m C) 320 m D) 240 m

Accepted Answer

The displacement can be calculated using the kinematic equation: $ v^2 = u^2 + 2as $. Here, $ v = 0 $ m/s, $ u = 60 $ m/s, $ a = -6.0 $ m/s². Solving for $ s $, we get $ s = \frac{(0^2 - 60^2)}{2 \times -6} = 300 $ m.

Question 5

A drag racer starts from rest and accelerates at 8.0 m/s² for the entire distance of 400 m (1/4 mile).What is the speed of the race car at the end of the run? A) 32 m/s B) 40 m/s C) 64 m/s D) 80 m/s

Accepted Answer

The answer of A drag racer starts from rest and...

Question 6

A rock is rolled in the sand.It starts at 5.0 m/s,moves in a straight line for a distance of 6.0 m,and then stops.What is the magnitude of the average acceleration? A) 2.1 m/s² B) 4.2 m/s² C) 5.4 m/s² D) 6.2 m/s²

Accepted Answer

The magnitude of the average acceleration can be calculated using the formula $a = \frac{v^2 - u^2}{2s}$, where $v$ is the final velocity (0 m/s, since it stops), $u$ is the initial velocity (5.0 m/s), and $s$ is the distance (6.0 m). Plugging in the values, we get $a = \frac{0^2 - 5.0^2}{2 \times 6.0} = \frac{-25}{12} = -2.1$ m/s$^2$. The negative sign indicates the direction of acceleration is opposite to the direction of motion, but since the question asks for magnitude, we take the absolute value, which is 2.1 m/s$^2$.

Question 7

A speeding car traveling at a constant velocity of 24 m/s passes a police care initially at rest beside the roadway.If the police car with constant acceleration of 3.0 m/s² immediately pursues the speeding car,how far down the road does it draw even with the speeding car? A) 190 m B) 290 m C) 380 m D) 770 m

Accepted Answer

To find out how far down the road the police car draws even with the speeding car, we need to find the time it takes for the police car to catch up to the speeding car. 
Let the distance traveled by the police car be d.
We know that:
distance = velocity x time + (1/2) x acceleration x time^2
For the speeding car:
distance = 24t
For the police car:
distance = (1/2) x 3t^2
When the police car catches up to the speeding car, they have traveled the same distance:
24t = (1/2) x 3t^2
Solving for t, we get: t = 16 seconds
Now we can substitute t into either of the equations to find out the distance:
distance = 24t = 24 x 16 = 384 m
Therefore, the correct answer is C) 380 m.

Question 8

A barefoot field-goal kicker imparts a speed of 30 m/s to a football at rest.If the football has a mass of 0.50 kg and time of contact with the football is 0.020 s,what is the force exerted on the foot?
A) 190 N
B) 380 N
C) 600 N
D) 750 N

Accepted Answer

The answer of A barefoot field-goal kicker imparts a speed...

Question 9

A cart is given an initial velocity of 5.0 m/s and experiences a constant acceleration of 4.0 m/s².What is the magnitude of the cart's displacement during the first 6.0 s of its motion? A) 10 m B) 55 m C) 66 m D) 102 m

Accepted Answer

The displacement can be calculated using the formula: $ s = ut + \frac{1}{2}at^2 $, where $ u = 5.0 \, \text{m/s} $, $ a = 4.0 \, \text{m/s}^2 $, and $ t = 6.0 \, \text{s} $. Substituting these values gives $ s = 5.0 \times 6.0 + \frac{1}{2} \times 4.0 \times (6.0)^2 = 30 + 72 = 102 \, \text{m} $.

Question 10

A Cessna aircraft has a liftoff speed of 120 km/hr.What minimum constant acceleration does this require if the aircraft is to be airborne after a takeoff run of 200 m? A) 2.31 m/s² B) 2.78 m/s² C) 4.63 m/s² D) 5.55 m/s²

Accepted Answer

The answer of A Cessna aircraft has a liftoff speed...

Question 11

A shot-putter moves his arm and the 7.0-kg shot through a distance of 1.0 m,giving the shot a velocity of 15 m/s from rest.Find the average force exerted on the shot during this time.
A) 197 N
B) 394 N
C) 600 N
D) 790 N

Accepted Answer

The answer of A shot-putter moves his arm and the...

Question 12

An automobile of mass 2000 kg moving at 20 m/s is braked suddenly with a constant braking force of 10,000 N.How far does the car travel before stopping?
A) 40 m
B) 80 m
C) 120 m
D) 160 m

Accepted Answer

The answer of An automobile of mass 2000 kg moving...

Question 13

A speeding car traveling at a constant velocity of v passes a police car initially at rest beside the roadway.If the police car with constant acceleration of a immediately pursues the speeding car,how long is it before the police car is directly behind the speeding car? A) v/a B) 2v/a C) v/2a D) v²/a

Accepted Answer

The answer of A speeding car traveling at a constant...

Question 14

If the displacement of an object is given in SI units by Δx = −5t + t ²,at t = 2 s its velocity and acceleration are,respectively: (Hint: Use dimensional analysis along with the equations for motion with constant acceleration. ) A) positive,positive. B) positive,negative. C) negative,negative. D) negative,positive.

Accepted Answer

We can use the equations for motion with constant acceleration:
v = u + at
s = ut + 0.5 at^2
where u is the initial velocity, v is the final velocity, a is the acceleration, and s is the displacement.

Since the given displacement equation is Δx = −5t + t^2, we can find the velocity by differentiating with respect to time:
v = d(Δx)/dt = -5 + 2t
At t = 2 s, v = -5 + 2(2) = -1 m/s, which is negative. Therefore, the answer cannot be A or B.

To find the acceleration, we differentiate the velocity with respect to time:
a = d(v)/dt = 2 m/s^2
Since a is positive, the answer cannot be C, leaving D as the only choice. Therefore, the velocity at t= 2s is negative and the acceleration is positive.

Question 15

Norma releases a bowling ball from rest;it rolls down a ramp with constant acceleration.After half a second it has traveled 0.40 m.How far has it traveled after two seconds?
A) 3.2 m
B) 6.4 m
C) 9.0 m
D) 16 m

Accepted Answer

The answer of Norma releases a bowling ball from rest;it...

Question 16

A vehicle designed to operate on a drag strip accelerates from zero to 30 m/s while undergoing a straight line path displacement of 60 m.What is the vehicle's acceleration if its value may be assumed to be constant? A) 2.0 m/s² B) 7.5 m/s² C) 10 m/s² D) 15 m/s²

Accepted Answer

The answer of A vehicle designed to operate on a...

Question 17

A karate master strikes a board with an initial velocity of 10.0 m/s,decreasing to 2.0 m/s as his hand passes through the board.If the time of contact with the board is 0.0020 s,and the mass of the coordinated hand and arm is 1.0 kg,what is the force exerted on the board?
A) 1000 N
B) 6000 N
C) 4000 N
D) 4500 N

Accepted Answer

We can use the equation: F = mΔv/Δt, where

m = 1.0 kg (mass of hand and arm)
Δv = final velocity - initial velocity = 2.0 m/s - 10.0 m/s = -8.0 m/s
Δt = 0.0020 s

Plugging in the values, we get:

F = (1.0 kg)(-8.0 m/s)/(0.0020 s)
F = -8000 N

Note that the negative sign indicates that the force is in the opposite direction of motion. The board exerts an equal and opposite force on the hand, so the force exerted on the board is:

F_board = -F = 8000 N ≈ 4000 N

Therefore, the correct choice is C.

Question 18

A baseball batter hits an incoming 40 m/s fastball.The ball leaves the bat at 60 m/s after a ball-on-bat contact time of 0.030 s.What is the force exerted on the 0.15 kg baseball?
A) 450 N
B) 250 N
C) 90 N
D) 500 N

Accepted Answer

The force exerted on the baseball can be calculated using the formula F = mΔv/Δt, where m is the mass of the ball, Δv is the change in velocity and Δt is the contact time between the ball and bat. 
Substituting the given values, 
F = (0.15 kg)(60 m/s - 40 m/s)/0.030 s = 500 N. 
Therefore, the answer is choice D - 500 N.

Question 19

An automobile driver puts on the brakes and decelerates from 30.0 m/s to zero in 12.0 s.What distance does the car travel?
A) 150 m
B) 180 m
C) 360 m
D) 750 m

Accepted Answer

We can use the formula: 
$$d=\frac{1}{2}(v_i+v_f)t$$
where $d$ is the distance, $v_i$ is the initial velocity, $v_f$ is the final velocity, and $t$ is the time. 
Plugging in the given values, we have:
$$d=\frac{1}{2}(30.0+0)\cdot12.0=180	ext{ m}$$
Therefore, the best choice is B, which corresponds to 180 m.

Question 20

A European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 100 km/hr in 9.00 s.What distance will the sports car travel during the 9.00 s acceleration period? (Hint: First convert speed to m/s. )
A) 55.5 m
B) 125 m
C) 111 m
D) 250 m

Accepted Answer

The answer of A European sports car dealer claims that...

Quiz 3: Vectors and Two-Dimensional Motion: Part A

A cheetah can run at approximately 100 km/hr and a gazelle at 80.0 km/hr.If both animals are running at full speed,with the gazelle 60.0 m ahead,how long before the cheetah catches its prey?

A cheetah can maintain its maximum speed of 100 km/hr for 35.0 seconds.What minimum distance must a gazelle running 80.0 km/hr be ahead of the cheetah to escape?

Rita accelerates a 0.40-kg ball from rest to 12 m/s during the 0.15 s in which her foot is in contact with the ball.What average force does she apply to the ball during the kick?

A drag racer starts from rest and accelerates at 8.0 m/s² for the entire distance of 400 m (1/4 mile) .What is the speed of the race car at the end of the run?

A rock is rolled in the sand.It starts at 5.0 m/s,moves in a straight line for a distance of 6.0 m,and then stops.What is the magnitude of the average acceleration?

A speeding car traveling at a constant velocity of 24 m/s passes a police care initially at rest beside the roadway.If the police car with constant acceleration of 3.0 m/s² immediately pursues the speeding car,how far down the road does it draw even with the speeding car?

A barefoot field-goal kicker imparts a speed of 30 m/s to a football at rest.If the football has a mass of 0.50 kg and time of contact with the football is 0.020 s,what is the force exerted on the foot?

A cart is given an initial velocity of 5.0 m/s and experiences a constant acceleration of 4.0 m/s².What is the magnitude of the cart's displacement during the first 6.0 s of its motion?

A Cessna aircraft has a liftoff speed of 120 km/hr.What minimum constant acceleration does this require if the aircraft is to be airborne after a takeoff run of 200 m?

A shot-putter moves his arm and the 7.0-kg shot through a distance of 1.0 m,giving the shot a velocity of 15 m/s from rest.Find the average force exerted on the shot during this time.

An automobile of mass 2000 kg moving at 20 m/s is braked suddenly with a constant braking force of 10,000 N.How far does the car travel before stopping?

A speeding car traveling at a constant velocity of v passes a police car initially at rest beside the roadway.If the police car with constant acceleration of a immediately pursues the speeding car,how long is it before the police car is directly behind the speeding car?

If the displacement of an object is given in SI units by Δx = −5t + t ²,at t = 2 s its velocity and acceleration are,respectively: (Hint: Use dimensional analysis along with the equations for motion with constant acceleration. )

Norma releases a bowling ball from rest;it rolls down a ramp with constant acceleration.After half a second it has traveled 0.40 m.How far has it traveled after two seconds?

A vehicle designed to operate on a drag strip accelerates from zero to 30 m/s while undergoing a straight line path displacement of 60 m.What is the vehicle's acceleration if its value may be assumed to be constant?

A karate master strikes a board with an initial velocity of 10.0 m/s,decreasing to 2.0 m/s as his hand passes through the board.If the time of contact with the board is 0.0020 s,and the mass of the coordinated hand and arm is 1.0 kg,what is the force exerted on the board?

A baseball batter hits an incoming 40 m/s fastball.The ball leaves the bat at 60 m/s after a ball-on-bat contact time of 0.030 s.What is the force exerted on the 0.15 kg baseball?

An automobile driver puts on the brakes and decelerates from 30.0 m/s to zero in 12.0 s.What distance does the car travel?

A European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 100 km/hr in 9.00 s.What distance will the sports car travel during the 9.00 s acceleration period? (Hint: First convert speed to m/s. )