Q: A speeder passes a police car at $$17.9\ \mathrm{m/s}$$ while the police car starts from rest and accelerates at $$4.51\ \mathrm{m/s^2$}. $$How long does it take for the police car to catch the speeder?

$$t = \frac{2v_{s}}{a_{p}} = \frac{2 \times 17.9}{4.51} = 7.94\ \mathrm{s}$$

Q: A runner moves with a constant acceleration. If her initial velocity is $$2.0\ \mathrm{m/s}$$ and her acceleration is $$1.0\ \mathrm{m/s^2$}$$, what is her velocity after $$5.0\ \mathrm{s}$$?

$$v = v_0$ + at = 2.0 + 1.0 \times 5.0 = 7.0\ \mathrm{m/s}$$

Question 1

A car starts from rest and accelerates uniformly at $$2.00\ \mathrm{m/s^2$}$$ for $$8.00\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + (2.00)(8.00) = 16.0\ \mathrm{m/s}$$

Question 2

A boat leaves a marina at $$1.50\ \mathrm{m/s}$$ and accelerates at $$2.40\ \mathrm{m/s^2$}$$ for $$5.00\ \mathrm{s}. $$How far does it travel in this time?

Accepted Answer

$$x = x_0$ + \frac{1}{2}(v_0$ + v)t = 0 + \frac{1}{2}(1.50 + 13.5)5.00 = 37.5\ \mathrm{m}$$

Question 3

A rock is dropped from rest from a height of $$1.25\ \mathrm{m} on $$the Moon, where $$g = 1.62\ \mathrm{m/s^2$}. $$What is its velocity just before it lands?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0) = 0 + 2(-1.62)(-1.25) = 4.05$$ \Rightarrow v = -2.01\ \mathrm{m/s}$$

Question 4

A drag racer starts from rest and accelerates at $$7.40\ \mathrm{m/s^2$}. $$How far does it travel in $$2.00\ \mathrm{s}$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$ = 0 + 0 + \frac{1}{2} 	imes 7.40 	imes (2.00)^2$ = 14.8\ \mathrm{m}$$

Question 5

A speeder passes a police car at $$17.9\ \mathrm{m/s}$$ while the police car starts from rest and accelerates at $$4.51\ \mathrm{m/s^2$}. $$How long does it take for the police car to catch the speeder?

Accepted Answer

$$t = \frac{2v_{s}}{a_{p}} = \frac{2 	imes 17.9}{4.51} = 7.94\ \mathrm{s}$$

Question 6

Which equation would you use to find the position of an object at time $$t if $$you know its initial position, initial velocity, and acceleration?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 7

A car is traveling east at $$23.0\ \mathrm{m/s}. $$After $$6.00\ \mathrm{s}$$, its velocity is $$8.0\ \mathrm{m/s}$$ east. What is its acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{8.0 - 23.0}{6.00} = -2.50\ \mathrm{m/s^2$}$$

Question 8

Which of the following best describes the area under a velocity vs. time graph?

Accepted Answer

It represents the displacement of the object.

Question 9

A car accelerates from $$10.0\ \mathrm{m/s} to$$ $$30.0\ \mathrm{m/s} in$$ $$4.00\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{30.0 - 10.0}{4.00} = 5.00\ \mathrm{m/s^2$}$$

Question 10

A runner moves with a constant acceleration. If her initial velocity is $$2.0\ \mathrm{m/s}$$ and her acceleration is $$1.0\ \mathrm{m/s^2$}$$, what is her velocity after $$5.0\ \mathrm{s}$$?

Accepted Answer

$$v = v_0$ + at = 2.0 + 1.0 	imes 5.0 = 7.0\ \mathrm{m/s}$$

Question 11

A cyclist starts from rest and accelerates at $$0.80\ \mathrm{m/s^2$}$$ for $$10.0\ \mathrm{s}. $$What is the total distance traveled?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$ = 0 + 0 + \frac{1}{2} 	imes 0.80 	imes (10.0)^2$ = 40.0\ \mathrm{m}$$

Question 12

A ball is thrown straight up with an initial velocity of $$15.0\ \mathrm{m/s}. $$What is the maximum height it reaches? (Assume $$g = 9.80\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$) \rightarrow 0 = $$(15.0)^2 + 2(-9.80)(x - 0$$) \rightarrow x = \frac{225}{19.6} = 11.5\ \mathrm{m}$$

Question 13

A car decelerates from $$20.0\ \mathrm{m/s} to $$rest in $$4.00\ \mathrm{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{0 - 20.0}{4.00} = -5.00\ \mathrm{m/s^2$}$$

Question 14

A train moves with a constant velocity of $$30.0\ \mathrm{m/s}$$ for $$2.00\ \mathrm{min}. $$What is the distance it travels?

Accepted Answer

$$x = x_0$ + v t = 0 + 30.0 	imes 120 = 3600\ \mathrm{m}$$

Question 15

A car accelerates from rest at $$3.00\ \mathrm{m/s^2$}$$ for $$10.0\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + 3.00 	imes 10.0 = 30.0\ \mathrm{m/s}$$

Question 16

A ball is thrown downward with an initial velocity of $$5.00\ \mathrm{m/s}$$ from a height of $$20.0\ \mathrm{m}. $$What is its velocity just before it hits the ground? (Take $$g = 9.80\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$) = $$(5.00)^2 + 2(9.80)(20.0) = 400 + 25 = 425$$ \Rightarrow v = 20.6\ \mathrm{m/s}$$

One-Dimensional Kinematics: Motion with Constant Acceleration

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