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?

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

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

$$v_x \u003c 0$$

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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