Motion (Kinematics) — Practice Quiz

A Physics cheat sheet for Motion (Kinematics) — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Final Velocity (Constant Acceleration): The final velocity \(v_f\) of an object is its initial velocity \(v_i\) plus the acceleration \(a\) multiplied by the time \(t\).

$$v_f = v_i + at$$

Displacement (Constant Acceleration): The displacement \(d\) of an object is its initial velocity \(v_i\) times time \(t\) plus half the acceleration \(a\) times the square of the time.

$$d = v_i t + \frac{1}{2}at^2$$

Velocity-Displacement Relationship: Relates the final velocity \(v_f\), initial velocity \(v_i\), constant acceleration \(a\), and displacement \(d\) without using time.

$$v_f^2 = v_i^2 + 2ad$$

Displacement with Average Velocity: The displacement \(d\) of an object is the average of its initial and final velocities multiplied by the time \(t\).

$$d = \frac{1}{2}(v_i + v_f)t$$

Average Speed: The total distance traveled divided by the total time elapsed.

$$\text{Average Speed} = \frac{\text{Distance}}{\text{Elapsed Time}}$$

Relative Velocity: The velocity of object A relative to object C is the vector sum of the velocity of A relative to B and the velocity of B relative to C.

$$\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}$$

Projectile Motion (Horizontal Displacement): The horizontal position \(x\) at time \(t\), assuming constant horizontal velocity \(v_{0x}\).

$$x = v_{0x}t$$

Projectile Motion (Vertical Displacement): The vertical position \(y\) at time \(t\), with initial vertical velocity \(v_{0y}\) and vertical acceleration \(a_y\).

$$y = v_{0y}t + \frac{1}{2}a_yt^2$$

Projectile Motion (Vertical Velocity): The vertical velocity \(v_y\) at time \(t\), given initial vertical velocity \(v_{0y}\) and vertical acceleration \(a_y\).

$$v_y = v_{0y} + a_yt$$

Practice quiz

  1. A car accelerates uniformly from rest. Which of the following best describes how its velocity changes over time?

    • It increases linearly with time, as described by $v_f = v_i + at$.
    • It increases quadratically with time, as described by $v_f = v_i + at^2$.
    • It remains constant, as described by $v_f = v_i$.
    • It decreases linearly with time, as described by $v_f = v_i - at$.

    Answer: It increases linearly with time, as described by $v_f = v_i + at$.

  2. An object starts from rest and accelerates at $3.0 \text{ m/s}^2$ for $5.0 \text{ s}$. What is its final velocity?

    • $7.5 \text{ m/s}$
    • $30.0 \text{ m/s}$
    • $15.0 \text{ m/s}$
    • $2.5 \text{ m/s}$

    Answer: $15.0 \text{ m/s}$

  3. A ball is thrown vertically upward with an initial velocity of $20.0 \text{ m/s}$. Assuming no air resistance and a constant downward acceleration due to gravity of $9.8 \text{ m/s}^2$, what is its displacement after $3.0 \text{ s}$?

    • $60.0 \text{ m}$
    • $15.9 \text{ m}$
    • $44.1 \text{ m}$
    • $-15.9 \text{ m}$

    Answer: $15.9 \text{ m}$

  4. A train traveling at $10.0 \text{ m/s}$ accelerates uniformly at $2.0 \text{ m/s}^2$ over a distance of $100.0 \text{ m}$. What is its final velocity?

    • $10.0 \text{ m/s}$
    • $20.0 \text{ m/s}$
    • $14.1 \text{ m/s}$
    • $22.4 \text{ m/s}$

    Answer: $22.4 \text{ m/s}$

  5. An object moves with constant acceleration. Which of the following expressions correctly represents its displacement $d$ in terms of initial velocity $v_i$, final velocity $v_f$, and time $t$?

    • $d = \frac{1}{2}(v_i + v_f)t$
    • $d = v_i t + \frac{1}{2}at^2$
    • $d = v_f t - \frac{1}{2}at^2$
    • $d = v_i t$

    Answer: $d = \frac{1}{2}(v_i + v_f)t$

  6. A runner completes a $400 \text{ m}$ race in $50 \text{ s}$. What is the runner's average speed?

    • $0.125 \text{ m/s}$
    • $20000 \text{ m/s}$
    • $8.0 \text{ m/s}$
    • $450 \text{ m/s}$

    Answer: $8.0 \text{ m/s}$

  7. A boat travels at $10 \text{ km/h}$ relative to the water. The water current flows at $3 \text{ km/h}$ relative to the shore. If the boat travels downstream (with the current), what is its speed relative to the shore?

    • $7 \text{ km/h}$
    • $13 \text{ km/h}$
    • $10 \text{ km/h}$
    • $3 \text{ km/h}$

    Answer: $13 \text{ km/h}$

  8. A projectile is launched horizontally from a cliff $45 \text{ m}$ high with an initial horizontal velocity of $15 \text{ m/s}$. How long does it take for the projectile to hit the ground? (Assume acceleration due to gravity $a_y = 9.8 \text{ m/s}^2$ downwards).

    • $3.03 \text{ s}$
    • $1.5 \text{ s}$
    • $4.5 \text{ s}$
    • $9.8 \text{ s}$

    Answer: $3.03 \text{ s}$

  9. For the projectile described in the previous question (launched horizontally from a cliff $45 \text{ m}$ high with an initial horizontal velocity of $15 \text{ m/s}$), what is its horizontal displacement when it hits the ground?

    • $15.0 \text{ m}$
    • $30.0 \text{ m}$
    • $45.5 \text{ m}$
    • $67.5 \text{ m}$

    Answer: $45.5 \text{ m}$

  10. An object is dropped from a height. What is its vertical velocity after $2.0 \text{ s}$? (Assume acceleration due to gravity $a_y = 9.8 \text{ m/s}^2$ downwards).

    • $9.8 \text{ m/s}$
    • $4.9 \text{ m/s}$
    • $0 \text{ m/s}$
    • $19.6 \text{ m/s}$

    Answer: $19.6 \text{ m/s}$

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