Q: A car with an initial velocity of $$25\ \mathrm{m/s}$$ accelerates uniformly at $$2.2\ \mathrm{m/s^2$}$$ for $$4.5\ \mathrm{s}. $$What is the car's final velocity?

$$v = 25 + (2.2 \times 4.5) = 34.9\ \mathrm{m/s}$$

Q: A bullet leaves a rifle barrel of length $$0.80\ \mathrm{m}$$ with a speed of $$550\ \mathrm{m/s}. $$What is the acceleration of the bullet while in the barrel?

$$a = \frac{v^2$}{2d} = \frac{550^2$}{2 \times 0.80} = 189,062.5\ \mathrm{m/s^2$}$$

Q: A plane travels $$600\ \mathrm{m}$$ while being accelerated uniformly from rest at $$4.5\ \mathrm{m/s^2$}. $$How long does it take to travel this distance?

$$t = \sqrt{\frac{2d}{a}} = \sqrt{\frac{2 \times 600}{4.5}} = 16.3\ \mathrm{s}$$

Q: A stone is dropped from a tower $$150\ \mathrm{m}$$ high. What is the speed of the stone when it strikes the ground?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 150} = 54.2\ \mathrm{m/s}$$

Q: A jet lands on a runway at $$180\ \mathrm{m/s}$$ and decelerates at $$-9\ \mathrm{m/s^2$}$$ until it stops. What is the stopping distance?

$$d = \frac{v^2$}{2a} = \frac{(180)^2$}{2 \times 9} = 1800\ \mathrm{m}$$

Q: A ball is thrown upward and remains in the air for $$14\ \mathrm{s}. $$What was the initial speed with which it was thrown?

$$v_0$$ = \frac{gt}{2} = \frac{9.8 \times 14}{2} = 68.6\ \mathrm{m/s}$$

Q: A rocket accelerates from rest at $$8.00\ \mathrm{m/s^2$}$$ for $$60.0\ \mathrm{s}. $$What is the rocket’s velocity when the engine is shut off?

$$v = at = 8.00 \times 60.0 = 480\ \mathrm{m/s}$$

Question 1

A car moves with an initial velocity of $$+10\ \mathrm{m/s}$$ and after a short time interval, its velocity changes as shown in the images above (A, B, C, D). In which scenario does the car experience the greatest magnitude of change in velocity?

Accepted Answer

Scenario C: $$+10\ \mathrm{m/s} to$$ $$-20\ \mathrm{m/s}$$

Question 2

Link walks 5 miles east, then 7 miles north, then 2 miles south. What is his total displacement?

Accepted Answer

$$\sqrt{(5^2$ + 5^2$)} = 7.07$$ miles east-north

Question 3

A car with an initial velocity of $$25\ \mathrm{m/s}$$ accelerates uniformly at $$2.2\ \mathrm{m/s^2$}$$ for $$4.5\ \mathrm{s}. $$What is the car's final velocity?

Accepted Answer

$$v = 25 + (2.2 	imes 4.5) = 34.9\ \mathrm{m/s}$$

Question 4

A bullet leaves a rifle barrel of length $$0.80\ \mathrm{m}$$ with a speed of $$550\ \mathrm{m/s}. $$What is the acceleration of the bullet while in the barrel?

Accepted Answer

$$a = \frac{v^2$}{2d} = \frac{550^2$}{2 	imes 0.80} = 189,062.5\ \mathrm{m/s^2$}$$

Question 5

A plane travels $$600\ \mathrm{m}$$ while being accelerated uniformly from rest at $$4.5\ \mathrm{m/s^2$}. $$How long does it take to travel this distance?

Accepted Answer

$$t = \sqrt{\frac{2d}{a}} = \sqrt{\frac{2 	imes 600}{4.5}} = 16.3\ \mathrm{s}$$

Question 6

Refer to the velocity vs. time graph above. What is the acceleration of the object at $$t = 4\ \mathrm{s}$$?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{-8 - 20}{8 - 0} = -3.5\ \mathrm{m/s^2$}$$

Question 7

A stone is dropped from a tower $$150\ \mathrm{m}$$ high. What is the speed of the stone when it strikes the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 150} = 54.2\ \mathrm{m/s}$$

Question 8

A jet lands on a runway at $$180\ \mathrm{m/s}$$ and decelerates at $$-9\ \mathrm{m/s^2$}$$ until it stops. What is the stopping distance?

Accepted Answer

$$d = \frac{v^2$}{2a} = \frac{(180)^2$}{2 	imes 9} = 1800\ \mathrm{m}$$

Question 9

Refer to the position vs. time graph above. At which point is the object at rest?

Accepted Answer

Point B

Question 10

Refer to the velocity vs. time graph above (with labeled points A-H). At which point is the acceleration negative and the instantaneous speed increasing?

Accepted Answer

Point F

Question 11

A ball is thrown upward and remains in the air for $$14\ \mathrm{s}. $$What was the initial speed with which it was thrown?

Accepted Answer

$$v_0$$ = \frac{gt}{2} = \frac{9.8 	imes 14}{2} = 68.6\ \mathrm{m/s}$$

Question 12

A car starts from rest and covers a distance $$D$$ while accelerating to a final velocity $$V. $$What is the expression for the car’s acceleration?

Accepted Answer

$$a = \frac{V^2$}{2D}$$

Question 13

A rocket accelerates from rest at $$8.00\ \mathrm{m/s^2$}$$ for $$60.0\ \mathrm{s}. $$What is the rocket’s velocity when the engine is shut off?

Accepted Answer

$$v = at = 8.00 	imes 60.0 = 480\ \mathrm{m/s}$$

Question 14

A bullet leaves a rifle barrel of length $$0.80\ \mathrm{m}$$ with a speed of $$550\ \mathrm{m/s}. $$For how long is the bullet in the barrel?

Accepted Answer

$$t = \frac{v}{a} = \frac{550}{189062.5} = 0.00291\ \mathrm{s}$$

Step-by-Step Guidance for AP Physics 1 Unit 1 Kinematics and Kinematic Graphs

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