Question 1

A car accelerates from rest with a constant acceleration $a$ for a time $t$. Which equation correctly gives the displacement $x$ of the car during this time?

Accepted Answer

$x = v_0 t + \frac{1}{2} a t^2$

Question 2

A ball is dropped from rest from a tall building. Neglecting air resistance, which of the following best describes the velocity of the ball after it has fallen for time $t$?

Accepted Answer

$v = v_0 + g t$

Question 3

Which of the following statements about reference frames is correct?

Accepted Answer

The velocity of an object can be different depending on the chosen reference frame.

Question 4

A driver sees a red light and slams on the brakes, coming to a stop from an initial velocity $v_0$ over a distance $d$ with constant acceleration $a$. Which kinematic equation would you use to solve for the acceleration?

Accepted Answer

$v^2 = v_0^2 + 2 a d$

Question 5

If the velocity of an object is given by $v(t)$, how do you find the change in position $\Delta x$ over a time interval $t_1$ to $t_2$?

Accepted Answer

$\Delta x = \int_{t_1}^{t_2} v(t) \, dt$

Question 6

A ball is thrown vertically upward with initial velocity $v_0$. Ignoring air resistance, what is the acceleration of the ball at its highest point?

Accepted Answer

$a = -g$

Question 7

Which of the following is the correct definition of instantaneous acceleration?

Accepted Answer

$a = \frac{dv}{dt}$

Question 8

A ball is dropped from rest and passes three windows as it falls. Which window does the ball spend the most time passing?

Accepted Answer

The highest window, because the ball is moving slowest there.

Question 9

A NASA drop tower releases an object from rest and it falls freely for $2.5$ seconds. What is the final velocity of the object just before it hits the bottom? (Assume $g = 9.8 	ext{ m/s}^2$)

Accepted Answer

$v = 24.5 	ext{ m/s}$

Question 10

Which of the following is NOT a correct kinematic equation for motion with constant acceleration?

Accepted Answer

$x = x_0 + v_0 t + a t^3$

Question 11

A car moves with constant acceleration. Which graph best represents its velocity as a function of time?

Accepted Answer

A straight line with positive slope.

Question 12

If an object moves in the negative direction with a positive acceleration, what happens to its speed?

Accepted Answer

Its speed decreases.

Question 13

Which of the following is the correct expression for the acceleration due to gravity at the surface of a planet of mass $M$ and radius $R$?

Accepted Answer

$g = \frac{G M}{R^2}$

Question 14

A student analyzes the motion of a cart using two different reference frames: one fixed to the track and one moving with the cart. What will be the measured velocity of the cart in the moving reference frame?

Accepted Answer

Zero, because the cart is at rest relative to the moving frame.

Question 15

Which of the following best describes the area under a velocity vs. time graph between $t_1$ and $t_2$?

Accepted Answer

It represents the change in position $\Delta x$.

Question 16

A ball is thrown downward with initial velocity $v_0$ from a height $h$. What is the equation for its position $y$ as a function of time $t$, taking downward as the positive direction?

Accepted Answer

$y = y_0 + v_0 t + \frac{1}{2} g t^2$

Question 17

Which of the following is a correct procedure for solving kinematics problems?

Accepted Answer

Carefully analyze the information, choose a coordinate axis, and use appropriate equations.

Question 18

An object moves with constant acceleration $a$. If its initial velocity is $v_0$ and its final velocity after time $t$ is $v$, which equation relates these quantities?

Accepted Answer

$v = v_0 + a t$

Question 19

A ball is thrown upward and returns to its starting point. Which of the following statements is true about its velocity and acceleration at the highest point?

Accepted Answer

Velocity is zero, acceleration is $-g$.

PHYS 2110: Mechanics – Motion with Constant Acceleration and Reference Frames

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