Momentum and Impulse — Practice Quiz

A Physics cheat sheet for Momentum and Impulse — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Impulse: The impulse \(\vec{J}\) is the product of the average force \(\vec{F}\) and the time interval \(\Delta t\).

$$\vec{J} = \vec{F}\Delta t$$

Linear Momentum: The linear momentum \(\vec{p}\) is the product of mass \(m\) and velocity \(\vec{v}\).

$$\vec{p} = m\vec{v}$$

Impulse-Momentum Theorem: The impulse applied to an object equals its change in momentum.

$$(\sum \vec{F})\Delta t = m\vec{v}_f - m\vec{v}_0$$

Conservation of Linear Momentum: The total linear momentum of an isolated system remains constant.

$$m_1\vec{v}_{f1} + m_2\vec{v}_{f2} = m_1\vec{v}_{01} + m_2\vec{v}_{02}$$

Center of Mass (Position): The coordinate \(x_{cm}\) of the center of mass for a two-particle system.

$$x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$$

Velocity of Center of Mass: The velocity \(v_{cm}\) of the center of mass for a two-particle system.

$$v_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$$

Practice quiz

  1. A $5 \text{ kg}$ object experiences a net force of $20 \text{ N}$ for $3 \text{ s}$. What is the magnitude of the impulse applied to the object?

    • $60 \text{ N} \cdot \text{s}$
    • $100 \text{ N} \cdot \text{s}$
    • $15 \text{ N} \cdot \text{s}$
    • $4 \text{ N} \cdot \text{s}$

    Answer: $60 \text{ N} \cdot \text{s}$

  2. A $2 \text{ kg}$ ball is moving with a velocity of $10 \text{ m/s}$ to the east. What is the magnitude of its linear momentum?

    • $20 \text{ kg} \cdot \text{m/s}$
    • $5 \text{ kg} \cdot \text{m/s}$
    • $0.2 \text{ kg} \cdot \text{m/s}$
    • $12 \text{ kg} \cdot \text{m/s}$

    Answer: $20 \text{ kg} \cdot \text{m/s}$

  3. A $0.5 \text{ kg}$ ball initially moving at $10 \text{ m/s}$ is hit by a bat, reversing its direction and increasing its speed to $15 \text{ m/s}$. What is the magnitude of the impulse delivered by the bat?

    • $2.5 \text{ N} \cdot \text{s}$
    • $7.5 \text{ N} \cdot \text{s}$
    • $12.5 \text{ N} \cdot \text{s}$
    • $1.25 \text{ N} \cdot \text{s}$

    Answer: $12.5 \text{ N} \cdot \text{s}$

  4. A $2 \text{ kg}$ cart moving at $3 \text{ m/s}$ collides head-on with a stationary $4 \text{ kg}$ cart. If the two carts stick together after the collision, what is their common final velocity?

    • $1 \text{ m/s}$
    • $0.5 \text{ m/s}$
    • $1.5 \text{ m/s}$
    • $2 \text{ m/s}$

    Answer: $1 \text{ m/s}$

  5. A $3 \text{ kg}$ mass is located at $x=0 \text{ m}$ and a $2 \text{ kg}$ mass is located at $x=5 \text{ m}$. Where is the center of mass of this two-particle system?

    • $x=2 \text{ m}$
    • $x=2.5 \text{ m}$
    • $x=3 \text{ m}$
    • $x=1 \text{ m}$

    Answer: $x=2 \text{ m}$

  6. A $1 \text{ kg}$ particle moves at $4 \text{ m/s}$ and a $3 \text{ kg}$ particle moves in the same direction at $2 \text{ m/s}$. What is the velocity of the center of mass of this system?

    • $2.5 \text{ m/s}$
    • $3 \text{ m/s}$
    • $2.75 \text{ m/s}$
    • $2.25 \text{ m/s}$

    Answer: $2.5 \text{ m/s}$

  7. To minimize the force experienced during a collision, one should:

    • Decrease the time interval of the collision.
    • Increase the time interval of the collision.
    • Decrease the change in momentum.
    • Increase the mass of the object.

    Answer: Increase the time interval of the collision.

  8. A $60 \text{ kg}$ person standing on ice throws a $0.5 \text{ kg}$ ball horizontally with a speed of $10 \text{ m/s}$. Assuming no friction, what is the recoil speed of the person?

    • $0.083 \text{ m/s}$
    • $0.167 \text{ m/s}$
    • $0.5 \text{ m/s}$
    • $0.042 \text{ m/s}$

    Answer: $0.083 \text{ m/s}$

  9. A $0.15 \text{ kg}$ baseball initially moving at $40 \text{ m/s}$ is caught by a catcher's mitt. If the ball comes to rest in $0.02 \text{ s}$, what is the magnitude of the average force exerted by the mitt on the ball?

    • $300 \text{ N}$
    • $150 \text{ N}$
    • $600 \text{ N}$
    • $75 \text{ N}$

    Answer: $300 \text{ N}$

  10. In an isolated system of two particles, if the first particle has a mass $m_1$ and velocity $v_1$, and the second particle has a mass $m_2$ and velocity $v_2$, what happens to the velocity of the center of mass ($v_{cm}$) if an internal force acts between the particles?

    • $v_{cm}$ increases.
    • $v_{cm}$ decreases.
    • $v_{cm}$ remains constant.
    • $v_{cm}$ changes direction.

    Answer: $v_{cm}$ remains constant.

Select a subject

Select a subject from the left panel to begin exploring formulas.