Question 1

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 5 + 4t + 3t^2$. What is the car's instantaneous velocity at t = 2$ s?

Accepted Answer

$$v = 4 + 6t = 16 m/s$$

Question 2

Which of the following statements about instantaneous velocity is correct?

Accepted Answer

It is the slope of the tangent to the $$x$$-$$t$$ graph at a given time.

Question 3

A turtle and a rabbit are to have a race. The turtle’s average speed is $$0.9 m/s$$, the rabbit’s average speed is $$9 m/s$$, and the race distance is $$1500 m. $$What is the maximum time (in minutes) the rabbit can wait before starting to run and still win the race?

Accepted Answer

20 minutes

Question 4

Which equation gives the position $$x of an $$object moving with constant acceleration $$a$$, initial velocity $$v_0$$, after time $$t$$?

Accepted Answer

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

Question 5

A small block slides down a frictionless incline with constant acceleration. It is released from rest at the top, and its speed after traveling $$6.80 m is$$ $$3.80 m/s. $$What is its speed after traveling $$3.40 m$$?

Accepted Answer

$$v = 2.69 m/s$$

Question 6

Which of the following is the correct formula for velocity as a function of time for motion with constant acceleration?

Accepted Answer

$$v = v_0$ + a t$$

Question 7

A rock is thrown straight up from a bridge and passes you on its way down $$6.00 s $$after it was thrown. If the rock falls $$28.0 m $$below the point where it was released, what is its speed just before it hits the water? (Ignore air resistance.)

Accepted Answer

$$v = 37.6 m/s$$

Question 8

For a freely falling body near Earth's surface, what is the value and direction of acceleration if upward is chosen as positive?

Accepted Answer

$$a = -9.8 m/s$^2$$, downward

Question 9

An antelope moving with constant acceleration covers $$70.0 m in$$ $$7.00 s. $$Its speed as it passes the second point is $$15.0 m/s. $$What was its speed at the first point?

Accepted Answer

$$v_0 = 5.0$ m/s

Question 10

Which of the following is NOT a correct equation of motion for constant acceleration?

Accepted Answer

$$x = v_0$ + a t^2$

Question 11

The area under a velocity-time ($$v$$-$$t) $$graph between $$t_0$$ and $$t_1$$ represents:

Accepted Answer

The displacement of the object

Question 12

A police car traveling at $$95 km/h is $$passed by a speeder at $$135 km/h. $$One second after the speeder passes, the police accelerates at $$2.60 m/s$^2. $$How much time passes before the police overtakes the speeder?

Accepted Answer

16.5 s

Question 13

Which of the following best describes average acceleration?

Accepted Answer

$$a_{ave} = \frac{v - v_0$}{t}$$

Question 14

If the velocity of a car is constant, which of the following is true about its acceleration?

Accepted Answer

Acceleration is zero.

Question 15

A train travels at $$75 km/h $$and a car at $$95 km/h. If $$the train is $$1.50 km $$long, how long does it take the car to pass the train?

Accepted Answer

4.5 minutes

Question 16

Which of the following is the correct expression for instantaneous acceleration?

Accepted Answer

$$a = \frac{d^2$ x}{dt^2$}$$

Question 17

For a body in free fall, which equation relates its final velocity $$v to $$its initial velocity $$v_0$$, acceleration $$g$$, and displacement $$y - y_0$?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2g(y$$ - $$y_0$$)$$

Question 18

The change in velocity of an object is represented graphically by:

Accepted Answer

The area under the $$a$$-$$t$$ graph

Question 19

Which of the following is true for motion with constant acceleration?

Accepted Answer

Average acceleration equals instantaneous acceleration.

Kinematics in One Dimension: Motion Along a Straight Line

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