Q: A speedboat has a constant acceleration of $2.0\ \mathrm{m/s^2}$ and an initial velocity of $6.0\ \mathrm{m/s}$. What is its displacement after $8.0\ \mathrm{s}$?

$x = 6.0 \times 8.0 + \frac{1}{2} \times 2.0 \times 8.0^2 = 48 + 64 = 112\ \mathrm{m}$

Q: A cyclist maintains a constant velocity of $+10\ \mathrm{m/s}$ for $5\ \mathrm{s}$, stops for $2\ \mathrm{s}$, then returns at $-8\ \mathrm{m/s}$ for $5\ \mathrm{s}$. What is the total displacement?

$10 \times 5 + (-8) \times 5 = 50 - 40 = 10\ \mathrm{m}$

Q: Which statement about acceleration is correct?

Acceleration is the rate of change of velocity.

Question 1

A car travels from $x_0 = -5\ \mathrm{m}$ to $x = 15\ \mathrm{m}$ in $4\ \mathrm{s}$. What is the car's average velocity?

Accepted Answer

$\displaystyle \frac{15 - (-5)}{4} = 5\ \mathrm{m/s}$

Question 2

Which of the following statements about displacement is correct?

Accepted Answer

Displacement is a vector that points from the initial position to the final position.

Question 3

A runner starts at $x_0 = 0\ \mathrm{m}$ and runs to $x = 100\ \mathrm{m}$ in $10\ \mathrm{s}$, then returns to $x = 40\ \mathrm{m}$ in $5\ \mathrm{s}$. What is the runner's average velocity for the entire trip?

Accepted Answer

$\displaystyle \frac{40}{15} = 2.67\ \mathrm{m/s}$

Question 4

If a car's velocity changes from $+20\ \mathrm{m/s}$ to $-10\ \mathrm{m/s}$ in $5\ \mathrm{s}$, what is its average acceleration?

Accepted Answer

$-4\ \mathrm{m/s^2}$

Question 5

A jet plane starts from rest and accelerates at $a = +31\ \mathrm{m/s^2}$ to reach a velocity of $v = +62\ \mathrm{m/s}$. What is the displacement during this acceleration?

Accepted Answer

$\displaystyle x = \frac{v^2 - v_0^2}{2a} = \frac{62^2 - 0^2}{2 	imes 31} = 62\ \mathrm{m}$

Question 6

Which kinematic equation is independent of time?

Accepted Answer

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

Question 7

A speedboat has a constant acceleration of $2.0\ \mathrm{m/s^2}$ and an initial velocity of $6.0\ \mathrm{m/s}$. What is its displacement after $8.0\ \mathrm{s}$?

Accepted Answer

$x = 6.0 	imes 8.0 + \frac{1}{2} 	imes 2.0 	imes 8.0^2 = 48 + 64 = 112\ \mathrm{m}$

Question 8

A nerve impulse travels at $100\ \mathrm{m/s}$ through a human body of height $2\ \mathrm{m}$. Estimate the time it takes for the impulse to travel from the toe to the brain.

Accepted Answer

$0.02\ \mathrm{s}$

Question 9

On a velocity-time graph, what does the area under the curve represent?

Accepted Answer

The object's displacement

Question 10

A car travels to the left (negative direction) with an initial speed of $27\ \mathrm{m/s}$ and a final speed of $29\ \mathrm{m/s}$ over $5.0\ \mathrm{s}$. What is the car's acceleration and is it speeding up or slowing down?

Accepted Answer

$a = \frac{29 - 27}{5} = 0.4\ \mathrm{m/s^2}$, speeding up in the negative direction

Question 11

A jet plane has a takeoff speed of $v_0 = 75\ \mathrm{m/s}$ and can accelerate at $a = 1.3\ \mathrm{m/s^2}$. If the runway is $2.5\ \mathrm{km}$ long, can the plane safely take off?

Accepted Answer

No, because the required distance is $x = \frac{v^2}{2a} = \frac{75^2}{2 	imes 1.3} = 2163\ \mathrm{m}$, which is less than $2500\ \mathrm{m}$.

Question 12

Which of the following best describes instantaneous velocity?

Accepted Answer

The rate of change of position at a specific instant

Question 13

If an object moves in the negative $x$-direction, which statement is true about its velocity?

Accepted Answer

$v_x < 0$

Question 14

A cyclist maintains a constant velocity of $+10\ \mathrm{m/s}$ for $5\ \mathrm{s}$, stops for $2\ \mathrm{s}$, then returns at $-8\ \mathrm{m/s}$ for $5\ \mathrm{s}$. What is the total displacement?

Accepted Answer

$10 	imes 5 + (-8) 	imes 5 = 50 - 40 = 10\ \mathrm{m}$

Question 15

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

Accepted Answer

Force, $F$

Question 16

A car moves with a constant velocity of $15\ \mathrm{m/s}$ for $10\ \mathrm{s}$. What is its displacement?

Accepted Answer

$150\ \mathrm{m}$

Question 17

Which statement about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity.

Question 18

On a position-time graph, what does the slope represent?

Accepted Answer

Velocity

Question 19

A car starts at $x_0 = -16\ \mathrm{m}$ at $t = 0\ \mathrm{s}$ and travels in the $+x$ direction at a constant velocity for $18\ \mathrm{s}$, ending at $x = 20\ \mathrm{m}$. What is its velocity?

Accepted Answer

$\displaystyle \frac{20 - (-16)}{18} = 2\ \mathrm{m/s}$

Kinematics in One Dimension: Position, Velocity, and Acceleration

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