Q: A car moves along a straight road with constant acceleration. If its initial velocity is $v_0 = 2\ \mathrm{m/s}$ and its acceleration is $a = 3\ \mathrm{m/s^2}$, what is its velocity after $4\ \mathrm{s}$?

$v = v_0 + at = 2 + 3 \times 4 = 14\ \mathrm{m/s}$

Q: A runner accelerates from rest at $a = 2\ \mathrm{m/s^2}$ for $5\ \mathrm{s}$. What is the runner's displacement during this time?

$x = x_0 + v_0 t + \frac{1}{2} a t^2 = 0 + 0 + \frac{1}{2} \times 2 \times 25 = 25\ \mathrm{m}$

Q: A ball is thrown straight up with an initial velocity of $10\ \mathrm{m/s}$. Neglecting air resistance, what is its velocity after $2\ \mathrm{s}$? (Take $a = -9.8\ \mathrm{m/s^2}$)

$v = v_0 + a t = 10 + (-9.8) \times 2 = -9.6\ \mathrm{m/s}$

Q: A car starts from rest and accelerates at $a = 4\ \mathrm{m/s^2}$ for $3\ \mathrm{s}$. What is its final velocity?

$v = v_0 + a t = 0 + 4 \times 3 = 12\ \mathrm{m/s}$

Q: A cyclist moves with a constant velocity of $5\ \mathrm{m/s}$ for $10\ \mathrm{s}$. What is the total displacement?

$x = v t = 5 \times 10 = 50\ \mathrm{m}$

Question 1

A car moves along a straight road with constant acceleration. If its initial velocity is $v_0 = 2\ \mathrm{m/s}$ and its acceleration is $a = 3\ \mathrm{m/s^2}$, what is its velocity after $4\ \mathrm{s}$?

Accepted Answer

$v = v_0 + at = 2 + 3 	imes 4 = 14\ \mathrm{m/s}$

Question 2

Which of the following best describes the difference between displacement and distance traveled?

Accepted Answer

Displacement is a vector quantity representing the change in position, while distance traveled is a scalar quantity representing the total path length.

Question 3

A bug moves from $x_1 = 2.75\ \mathrm{m}$ to $x_2 = 2.25\ \mathrm{m}$ in $1\ \mathrm{s}$. What is its average velocity?

Accepted Answer

$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{2.25 - 2.75}{1} = -0.5\ \mathrm{m/s}$

Question 4

Which kinematic equation would you use to find the displacement of an object given its initial velocity, acceleration, and time?

Accepted Answer

$x = x_0 + v_0 t + \frac{1}{2} a t^2$

Question 5

A runner accelerates from rest at $a = 2\ \mathrm{m/s^2}$ for $5\ \mathrm{s}$. What is the runner's displacement during this time?

Accepted Answer

$x = x_0 + v_0 t + \frac{1}{2} a t^2 = 0 + 0 + \frac{1}{2} 	imes 2 	imes 25 = 25\ \mathrm{m}$

Question 6

If an object’s velocity changes from $4\ \mathrm{m/s}$ to $-2\ \mathrm{m/s}$ in $3\ \mathrm{s}$, what is its average acceleration?

Accepted Answer

$a_{avg} = \frac{\Delta v}{\Delta t} = \frac{-2 - 4}{3} = -2\ \mathrm{m/s^2}$

Question 7

Which of the following statements about motion diagrams is correct?

Accepted Answer

Motion diagrams use equally spaced dots to represent an object's position at equal time intervals.

Question 8

A ball is thrown straight up with an initial velocity of $10\ \mathrm{m/s}$. Neglecting air resistance, what is its velocity after $2\ \mathrm{s}$? (Take $a = -9.8\ \mathrm{m/s^2}$)

Accepted Answer

$v = v_0 + a t = 10 + (-9.8) 	imes 2 = -9.6\ \mathrm{m/s}$

Question 9

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

Accepted Answer

$v = \frac{dx}{dt}$

Question 10

A car starts from rest and accelerates at $a = 4\ \mathrm{m/s^2}$ for $3\ \mathrm{s}$. What is its final velocity?

Accepted Answer

$v = v_0 + a t = 0 + 4 	imes 3 = 12\ \mathrm{m/s}$

Question 11

Which of the following quantities is a scalar?

Accepted Answer

Elapsed time $\Delta t$

Question 12

A cyclist moves with a constant velocity of $5\ \mathrm{m/s}$ for $10\ \mathrm{s}$. What is the total displacement?

Accepted Answer

$x = v t = 5 	imes 10 = 50\ \mathrm{m}$

Question 13

Which equation gives the acceleration as the second derivative of position with respect to time?

Accepted Answer

$a(t) = \frac{d^2x}{dt^2}$

Question 14

A car travels $100\ \mathrm{m}$ in $20\ \mathrm{s}$, then $50\ \mathrm{m}$ in $10\ \mathrm{s}$ in the same direction. What is its average velocity for the entire trip?

Accepted Answer

$v_{avg} = \frac{100 + 50}{20 + 10} = \frac{150}{30} = 5\ \mathrm{m/s}$

Question 15

If the acceleration of an object is zero, which of the following statements is true?

Accepted Answer

The object's velocity is constant.

Question 16

A train slows down from $20\ \mathrm{m/s}$ to $5\ \mathrm{m/s}$ in $15\ \mathrm{s}$. What is its acceleration?

Accepted Answer

$a = \frac{5 - 20}{15} = -1\ \mathrm{m/s^2}$

Question 17

Which of the following is the correct formula for average acceleration?

Accepted Answer

$a_{avg} = \frac{\Delta v}{\Delta t}$

Question 18

A car accelerates from $0$ to $30\ \mathrm{m/s}$ in $10\ \mathrm{s}$. What is the car's acceleration?

Accepted Answer

$a = \frac{30 - 0}{10} = 3\ \mathrm{m/s^2}$

Question 19

Which of the following is true about speed and velocity?

Accepted Answer

Speed is the magnitude of velocity and is always positive.

Kinematics: Motion Diagrams and 1D Motion with Constant Acceleration

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