Question 1

A car starts from rest and accelerates uniformly at $$2.00\ \mathrm{m/s^2$}$$ for $$10.0\ \mathrm{s}. $$What is the final velocity of the car?

Accepted Answer

$$v = v_0$ + at = 0 + (2.00)(10.0) = 20.0\ \mathrm{m/s}$$

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 the boat travel during 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 the speed of the rock 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

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

Question 5

A speeder passes a stationary police car at $$17.9\ \mathrm{m/s}. $$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

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

Question 6

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

Accepted Answer

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

Question 7

A car is traveling east at $$23.0\ \mathrm{m/s}. If it $$accelerates at $$-2.50\ \mathrm{m/s^2$}$$ for $$6.00\ \mathrm{s}$$, what is its final velocity?

Accepted Answer

$$v = v_0$ + at = 23.0 + (-2.50)(6.00) = 8.0\ \mathrm{m/s}$$

Question 8

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

Accepted Answer

It represents the displacement of the object.

Question 9

A car accelerates from $$10.0\ \mathrm{m/s} to$$ $$30.0\ \mathrm{m/s}$$ over a distance of $$100\ \mathrm{m}. $$What is its acceleration?

Accepted Answer

$$a = \frac{v^2$ - v_0$^2}{2(x - x_0$)} = \frac{(30.0)^2$ - (10.0)^2$}{2(100)} = \frac{900 - 100}{200} = 4.00\ \mathrm{m/s^2$}$$

Question 10

A runner moves with a constant velocity of $$5.00\ \mathrm{m/s}$$ for $$12.0\ \mathrm{s}. $$What is the total displacement?

Accepted Answer

$$x = x_0$ + v t = 0 + (5.00)(12.0) = 60.0\ \mathrm{m}$$

Question 11

A cyclist starts from rest and accelerates at $$1.20\ \mathrm{m/s^2$}$$ for $$8.00\ \mathrm{s}. $$What is the cyclist's displacement?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$ = 0 + 0 + \frac{1}{2}(1.20)(8.00)^2$ = 38.4\ \mathrm{m}$$

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? (Take $$g = 9.80\ \mathrm{m/s^2$}$$ 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

Which of the following is NOT an assumption made when using the constant-acceleration equations of motion?

Accepted Answer

The acceleration changes with time.

Question 14

A car travels at $$15.0\ \mathrm{m/s}$$ for $$4.00\ \mathrm{s}$$, then accelerates at $$3.00\ \mathrm{m/s^2$}$$ for $$2.00\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 15.0 + (3.00)(2.00) = 21.0\ \mathrm{m/s}$$

Question 15

A train slows down from $$30.0\ \mathrm{m/s} to $$rest in $$1.00\ \mathrm{km}. $$What is its acceleration?

Accepted Answer

$$a = \frac{v^2$ - v_0$^2}{2(x - x_0$)} = \frac{0 - (30.0)^2$}{2(1000)} = -0.45\ \mathrm{m/s^2$}$$

One-Dimensional Kinematics: Motion with Constant Acceleration

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