Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which of the following correctly gives the time to reach maximum height?

$$t = \dfrac{v_0$ \sin \theta}{g}$$

Question 1

Which of the following quantities is NOT a vector?

Accepted Answer

Distance

Question 2

A train moves due east at $$16\ \mathrm{m/s}$$ relative to the ground. Leo runs on top of the train with a velocity of $$3.7\ \mathrm{m/s}$$ due east relative to the ground. What is Leo's velocity relative to the train?

Accepted Answer

$$12.3\ \mathrm{m/s}$$

Question 3

Refer to the position vs. time graph at point P (see image). What are the signs of the acceleration and velocity at point P?

Accepted Answer

$$a \u003e 0;\ v \u003c 0$$

Question 4

You drive 40 miles to your grandma’s house. Your car gets 30 miles per gallon, gas costs $2.80 per gallon, and your average speed is 55 miles per hour. What is the cost of driving to grandma’s house in dollars per second?

Accepted Answer

$$0.0006$$ per second

Question 5

A sprinter starts from rest and accelerates at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}$$, then runs at constant speed for $$15\ \mathrm{s}$$, and finally decelerates at $$4.0\ \mathrm{m/s^2$} to $$rest. What is the total distance covered?

Accepted Answer

$$187.5\ \mathrm{m}$$

Question 6

Two hobbits travel $$650\ \mathrm{mi}$$ due east and then $$1258\ \mathrm{mi}$$ southeast. What is the magnitude of their total displacement?

Accepted Answer

$$1778\ \mathrm{mi}$$

Question 7

A catapult launches a stone at $$45^\circ to $$barely clear a $$40\ \mathrm{m}$$ wall that is $$120\ \mathrm{m}$$ away. What is the minimum initial speed required? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$33.9\ \mathrm{m/s}$$

Question 8

A baseball is hit at $$60\ \mathrm{m/s} at an $$angle of $$60^\circ. $$You are $$25\ \mathrm{m}$$ away and throw your mitt straight up as soon as the ball is hit. What initial speed must you throw the mitt to catch the ball at the same height?

Accepted Answer

$$38.5\ \mathrm{m/s}$$

Question 9

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

Accepted Answer

Distance is the total path traveled; displacement is the straight-line vector from start to end.

Question 10

A car accelerates uniformly from $$10\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the acceleration?

Accepted Answer

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

Question 11

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which of the following correctly gives the time to reach maximum height?

Accepted Answer

$$t = \dfrac{v_0$ \sin 	heta}{g}$$

Question 12

A cyclist travels 3 km north, then 4 km east. What is the magnitude of the displacement?

Accepted Answer

$$5\ \mathrm{km}$$

Question 13

If an object’s velocity is zero at an instant, which of the following must be true?

Accepted Answer

None of the above.

Physics with Calculus: Kinematics, Vectors, and Projectile Motion Exam Guidance

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