1. momentum is defined as an objects mass times its velocity.
2. impulse is defined as the force exerted on an object times the time that the force lasts.
3. if the net external force acting on a system is zero, then the total momentum of the system is zero.
4. when two objects collide and stick together, the collision is said to be elastic.
5. perfectly elastic collisions between large objects are uncommon in the everyday world.
ple-choice (13 questions, 26 points)
6. if the momentum of an object changes and its mass remains constant,
a. then it is accelerating (or decelerating).
b. then there is an impulse acting on it.
c. then its velocity is changing.
d. then all of the above are true.
e. then all of the above are false.
7. the momentum change of an object is equal to the...
a. impulse acting on it.
b. velocity change of the object.
c. force acting on it.
d. force acting on it times its velocity.
e. objects mass times the force acting on it.
8. a moving freight car runs into an identical car at rest on the tracks. the cars couple together. compared to the velocity of the first car before the collision, the velocity of the combined cars after the collision is...
a. zero.
b. one-half as large.
c. the same.
d. twice as large.
9. the reason padded dashboards are used in cars is that they...
a. look and feel good
b. decrease the impulse in a collision.
c. increase the force of impact in a collision.
d. decrease the momentum of a collision.
e. increase the time of impact of a collision.

Question

1. momentum is defined as an objects mass times its velocity.
2. impulse is defined as the force exerted on an object times the time that the force lasts.
3. if the net external force acting on a system is zero, then the total momentum of the system is zero.
4. when two objects collide and stick together, the collision is said to be elastic.
5. perfectly elastic collisions between large objects are uncommon in the everyday world.
ple-choice (13 questions, 26 points)
6. if the momentum of an object changes and its mass remains constant,
 a. then it is accelerating (or decelerating).
 b. then there is an impulse acting on it.
 c. then its velocity is changing.
 d. then all of the above are true.
 e. then all of the above are false.
7. the momentum change of an object is equal to the...
 a. impulse acting on it.
 b. velocity change of the object.
 c. force acting on it.
 d. force acting on it times its velocity.
 e. objects mass times the force acting on it.
8. a moving freight car runs into an identical car at rest on the tracks. the cars couple together. compared to the velocity of the first car before the collision, the velocity of the combined cars after the collision is...
 a. zero.
 b. one-half as large.
 c. the same.
 d. twice as large.
9. the reason padded dashboards are used in cars is that they...
 a. look and feel good
 b. decrease the impulse in a collision.
 c. increase the force of impact in a collision.
 d. decrease the momentum of a collision.
 e. increase the time of impact of a collision.

Accepted Answer

### Question 6
# Brief Explanations:
- Recall the formula for momentum: $ p = mv $. If mass $ m $ is constant and momentum $ p $ changes, velocity $ v $ must change (so option c is true).
- A change in velocity means acceleration (or deceleration, since $ a=\frac{\Delta v}{\Delta t} $), so option a is true.
- Impulse is defined as the change in momentum ($ J=\Delta p $), so if momentum changes, there is an impulse acting on the object (option b is true). Thus, all of the above are true.
# Answer:
d. then all of the above are true.

### Question 7
# Brief Explanations:
The impulse - momentum theorem states that the impulse acting on an object is equal to the change in the object's momentum, i.e., $ J=\Delta p $. Option a matches this theorem. Option b is incorrect because momentum change is not equal to velocity change (it's related to mass - velocity change). Option c is incorrect as force is related to rate of momentum change ($ F = \frac{\Delta p}{\Delta t} $). Option d and e are also incorrect based on the definitions of impulse and momentum.
# Answer:
a. impulse acting on it.

### Question 8
# Explanation:
## Step 1: Apply the law of conservation of momentum
The law of conservation of momentum states that for a system with no external forces, the total initial momentum equals the total final momentum. Let the mass of each freight car be $ m $, the initial velocity of the first car be $ v $, and the initial velocity of the second car be $ 0 $ (at rest). The total initial momentum $ p_{i}=m\times v + m\times0=mv $.
## Step 2: Find the final momentum
After the collision, the two cars couple together, so the total mass is $ m + m = 2m $, and let the final velocity be $ v_{f} $. The total final momentum $ p_{f}=(2m)v_{f} $.
## Step 3: Equate initial and final momentum
Since $ p_{i}=p_{f} $, we have $ mv=(2m)v_{f} $. Solving for $ v_{f} $, we divide both sides by $ 2m $, so $ v_{f}=\frac{v}{2} $. This means the velocity of the combined cars is one - half as large as the velocity of the first car before the collision.
# Answer:
b. one - half as large.

### Question 9
# Brief Explanations:
Impulse $ J = F\Delta t=\Delta p $. In a collision, the change in momentum ($ \Delta p $) of a person hitting the dashboard is relatively constant (since mass and velocity change are fixed in a typical collision). Padded dashboards increase the time of impact ($ \Delta t $). From $ F=\frac{\Delta p}{\Delta t} $, if $ \Delta t $ increases, the force $ F $ of impact decreases. Option a is not a scientific reason. Option b is wrong because impulse ($ \Delta p $) is constant. Option c is wrong as we want to decrease force. Option d is wrong as momentum change is constant. Option e is correct as padded dashboards increase the time of impact.
# Answer:
e. Increase the time of impact of a collision.

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QUESTION IMAGE

Question

Explanation:

Question 6

Step 1: Apply the law of conservation of momentum

Step 2: Find the final momentum

Step 3: Equate initial and final momentum

Answer:

Question 7