Q: Which of the following is the correct definition of instantaneous velocity?

$V_x = \lim_{\Delta T \to 0} \frac{\Delta x}{\Delta T}$

Question 1

A car starts from rest and accelerates at $2\ \mathrm{m/s^2}$ for $5$ seconds. What is its final velocity?

Accepted Answer

$10\ \mathrm{m/s}$

Question 2

Which equation gives the position $x$ of an object moving with constant acceleration $a_x$ after time $T$, starting from initial position $x_0$ and initial velocity $V_{0x}$?

Accepted Answer

$x = x_0 + V_{0x} T + \frac{1}{2} a_x T^2$

Question 3

A train accelerates at $0.5\ \mathrm{m/s^2}$ for $60$ seconds, then moves at constant speed for $240$ seconds, and finally slows down at $-1.0\ \mathrm{m/s^2}$ for $30$ seconds. What is the train's speed at the end of the acceleration phase?

Accepted Answer

$30\ \mathrm{m/s}$

Question 4

Which of the following best describes 'free fall'?

Accepted Answer

Any motion where gravity is the only force acting on the object

Question 5

An object is thrown upward with initial velocity $V_{0y}$. Which equation gives its velocity after time $t$ under gravity $g$?

Accepted Answer

$V_y = V_{0y} - g t$

Question 6

A ball is dropped from a height of $20\ \mathrm{m}$ on Earth ($g = 9.81\ \mathrm{m/s^2}$). How long does it take to reach the ground? (Neglect air resistance)

Accepted Answer

$2.02\ \mathrm{s}$

Question 7

Which equation relates the final velocity squared to initial velocity squared, acceleration, and displacement for constant acceleration?

Accepted Answer

$V_x^2 = V_{0x}^2 + 2 a_x \Delta x$

Question 8

A runner moves with an initial velocity of $5\ \mathrm{m/s}$ and accelerates at $1\ \mathrm{m/s^2}$ for $10$ seconds. What is the total displacement?

Question 9

On the Moon, the acceleration due to gravity is $1.62\ \mathrm{m/s^2}$. If an astronaut drops a rock from rest, how far will it fall in $3$ seconds?

Accepted Answer

$7.29\ \mathrm{m}$

Question 10

Which of the following is the correct unit for acceleration?

Accepted Answer

$\mathrm{m/s^2}$

Question 11

A cyclist slows down from $12\ \mathrm{m/s}$ to $4\ \mathrm{m/s}$ in $4$ seconds. What is the acceleration?

Accepted Answer

$-2\ \mathrm{m/s^2}$

Question 12

Which scenario best represents 'slowing down' in terms of velocity and acceleration?

Accepted Answer

$V_{2x} - V_{1x} < 0$ and $a_x > 0$

Question 13

A stone is thrown vertically upward with $V_{0y} = 20\ \mathrm{m/s}$. How long does it take to reach its highest point? ($g = 9.81\ \mathrm{m/s^2}$)

Accepted Answer

$2.04\ \mathrm{s}$

Question 14

Which equation gives the position $y$ of an object under gravity after time $t$, starting from $y_0$ and initial velocity $V_{0y}$?

Accepted Answer

$y = y_0 + V_{0y} t - \frac{1}{2} g t^2$

Question 15

A train moves at a constant speed of $30\ \mathrm{m/s}$ for $240$ seconds. What is the distance covered during this interval?

Accepted Answer

$7200\ \mathrm{m}$

Question 16

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

Accepted Answer

$V_x = \lim_{\Delta T 	o 0} \frac{\Delta x}{\Delta T}$

Question 17

A ball is thrown downward with an initial velocity of $5\ \mathrm{m/s}$ from a height of $10\ \mathrm{m}$. How long does it take to hit the ground? ($g = 9.81\ \mathrm{m/s^2}$)

Accepted Answer

$0.85\ \mathrm{s}$

Question 18

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

Accepted Answer

$x = x_0 + a_x T$

Question 19

If an object moves with constant velocity, what is its acceleration?

Accepted Answer

$0\ \mathrm{m/s^2}$

Kinematics: Motion Along a Straight Line and Free Fall

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