Q: A hockey puck is given a constant deceleration of $$8 \ \mathrm{m/s^2$}$$ and comes to rest after traveling $$16 \ \mathrm{m}. $$What was its initial speed?

$$v_0$$ = \sqrt{2 a \Delta x} = \sqrt{2 \times 8 \times 16} = \sqrt{256} = 16 \ \mathrm{m/s}$$

Q: A driver reacts to a hazard in $$0.7 \ \mathrm{s}$$ while driving at $$30 \ \mathrm{m/s}. $$How far does the car travel before the brakes are applied?

$$\Delta x = v t = 30 \times 0.7 = 21 \ \mathrm{m}$$

Question 1

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

Accepted Answer

$$v_f = v_0$ + a t = 0 + (2)(5) = 10 \ \mathrm{m/s}$$

Question 2

A train travels at a constant speed of $$20 \ \mathrm{m/s}$$ for $$60 \ \mathrm{s}$$, then decelerates at $$3.5 \ \mathrm{m/s^2$}$$ until it stops. What is the total distance covered during the deceleration phase?

Accepted Answer

$$\Delta x = \frac{v_f^2$ - v_0$^2}{2a} = \frac{0^2$ - 20^2$}{2(-3.5)} = \frac{-400}{-7} \approx 57.1 \ \mathrm{m}$$

Question 3

Which of the following equations is NOT one of the four Uniformly Accelerated Motion (UAM) equations?

Accepted Answer

$$a = \frac{v_0$}{t}$$

Question 4

A hockey puck is given a constant deceleration of $$8 \ \mathrm{m/s^2$}$$ and comes to rest after traveling $$16 \ \mathrm{m}. $$What was its initial speed?

Accepted Answer

$$v_0$$ = \sqrt{2 a \Delta x} = \sqrt{2 	imes 8 	imes 16} = \sqrt{256} = 16 \ \mathrm{m/s}$$

Question 5

A bullet is accelerated uniformly from rest through a barrel of length $$0.8 \ \mathrm{m}$$ with an acceleration of $$4000 \ \mathrm{m/s^2$}. $$How long is the bullet accelerated through the barrel?

Accepted Answer

$$\Delta x = v_0$ t + \frac{1}{2} a t^2$ \Rightarrow 0.8 = 0 + 0.5 	imes 4000 	imes t^2$ \Rightarrow t^2$ = \frac{0.8}{2000} = 0.0004 \Rightarrow t = 0.02 \ \mathrm{s}$$

Question 6

A car is moving at $$30 \ \mathrm{m/s}$$ and decelerates at $$6 \ \mathrm{m/s^2$}$$ until it stops. How much time does it take to stop?

Accepted Answer

$$t = \frac{v_f - v_0$}{a} = \frac{0 - 30}{-6} = 5 \ \mathrm{s}$$

Question 7

Which variable is ignored when using the equation $$v_f^2$ = v_0$^2 + 2 a \Delta x$$?

Accepted Answer

Time ($$t)$$

Question 8

A driver reacts to a hazard in $$0.7 \ \mathrm{s}$$ while driving at $$30 \ \mathrm{m/s}. $$How far does the car travel before the brakes are applied?

Accepted Answer

$$\Delta x = v t = 30 	imes 0.7 = 21 \ \mathrm{m}$$

Question 9

If a car's velocity changes from $$-10 \ \mathrm{m/s} to$$ $$-30 \ \mathrm{m/s}$$, what is the sign of its acceleration?

Accepted Answer

Negative

Question 10

A truck moving at $$30 \ \mathrm{m/s}$$ comes to a stop after traveling $$150 \ \mathrm{m}$$ with constant acceleration. What is the magnitude of the acceleration?

Accepted Answer

$$a = \frac{v_f^2$ - v_0$^2}{2 \Delta x} = \frac{0^2$ - 30^2$}{2 	imes 150} = \frac{-900}{300} = -3 \ \mathrm{m/s^2$}$$

Question 11

Which of the following statements is TRUE about positive acceleration?

Accepted Answer

Positive acceleration means the velocity is becoming more positive or less negative.

Question 12

A car accelerates from $$10 \ \mathrm{m/s} to$$ $$30 \ \mathrm{m/s} in$$ $$4 \ \mathrm{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{30 - 10}{4} = 5 \ \mathrm{m/s^2$}$$

Question 13

Which equation would you use to solve for displacement when you know initial velocity, acceleration, and time?

Accepted Answer

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

Question 14

A runner accelerates at $$1.5 \ \mathrm{m/s^2$}$$ from rest for $$8 \ \mathrm{s}. $$What is the runner's displacement?

Accepted Answer

$$\Delta x = v_0$ t + \frac{1}{2} a t^2$ = 0 + 0.5 	imes 1.5 	imes 64 = 48 \ \mathrm{m}$$

Question 15

A cyclist moves at a constant velocity of $$12 \ \mathrm{m/s}$$ for $$25 \ \mathrm{s}. $$What is the total displacement?

Accepted Answer

$$\Delta x = v t = 12 	imes 25 = 300 \ \mathrm{m}$$

Question 16

A car travels at $$15 \ \mathrm{m/s}$$ for $$10 \ \mathrm{s}$$, then accelerates at $$2 \ \mathrm{m/s^2$}$$ for $$5 \ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v_f = v_0$ + a t = 15 + 2 	imes 5 = 25 \ \mathrm{m/s}$$

Question 17

A car moving at $$20 \ \mathrm{m/s}$$ slows down at $$4 \ \mathrm{m/s^2$}$$ until it stops. What distance does it cover while stopping?

Accepted Answer

$$\Delta x = \frac{v_f^2$ - v_0$^2}{2a} = \frac{0^2$ - 20^2$}{2(-4)} = \frac{-400}{-8} = 50 \ \mathrm{m}$$

Uniformly Accelerated Motion (UAM) and Kinematics: Study Notes

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