Q: The instantaneous velocity at time $$t is $$defined mathematically as:

$$\displaystyle v = \lim_{\Delta t \to 0} \frac{\Delta s}{\Delta t} = \frac{ds}{dt}$$

Question 1

A train moves along a straight track at a constant speed. Which of the following statements about its motion is correct?

Accepted Answer

Its position-versus-time graph is a straight line with a constant slope.

Question 2

An object moves with a constant velocity of $$3\ \mathrm{m/s} to $$the right. If its initial position is $$x_0 = 2$$\ \mathrm{m}$$ at t = 0$, what is its position at t = 5$$\ \mathrm{s}$$?

Accepted Answer

$$x = 17\ \mathrm{m}$$

Question 3

Which of the following best describes the meaning of the slope of a position-versus-time graph?

Accepted Answer

It represents the object's velocity.

Question 4

A car moves backward for $$2\ \mathrm{s} at$$ $$2.0\ \mathrm{m/s}$$, stops for $$2\ \mathrm{s}$$, then moves forward for $$2\ \mathrm{s} at$$ $$5.0\ \mathrm{m/s}. $$What is the car's total displacement after $$6\ \mathrm{s}$$?

Accepted Answer

$$6.0\ \mathrm{m}$$

Question 5

An ant zig-zags back and forth on a picnic table, traveling a total distance of $$50\ \mathrm{cm}$$ but ending $$30\ \mathrm{cm}$$ from its starting point. What are the ant's distance traveled and displacement?

Accepted Answer

$$50\ \mathrm{cm}$$	and $$30\ \mathrm{cm}$$

Question 6

The instantaneous velocity at time $$t is $$defined mathematically as:

Accepted Answer

$$\displaystyle v = \lim_{\Delta t 	o 0} \frac{\Delta s}{\Delta t} = \frac{ds}{dt}$$

Question 7

A position-versus-time graph for an object is a curve. What does the slope of the tangent line at any point on this curve represent?

Accepted Answer

The instantaneous velocity at that point.

Question 8

A car's velocity changes from $$0\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s} in$$ $$6.0\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$5.0\ \mathrm{m/s^2$}$$

Question 9

A ball is thrown straight up. At its highest point, what is the ball's instantaneous acceleration?

Accepted Answer

$$-9.80\ \mathrm{m/s^2$}$$

Question 10

A drag racer starts from rest and accelerates so that its velocity increases linearly from $$0 to$$ $$12\ \mathrm{m/s} in$$ $$3.0\ \mathrm{s}. $$What is the displacement during this time?

Accepted Answer

$$18\ \mathrm{m}$$

Question 11

A particle's position is given by $$s(t) = 2t^2$ (in meters, with t$ in seconds). What is its velocity as a function of time?

Accepted Answer

$$v(t) = 4t$$

Question 12

A car moves with a velocity $$v(t) = 4t (in m/s). $$What is the displacement between $$t = 0$$ and $$t = 3\ \mathrm{s}$$?

Accepted Answer

$$18\ \mathrm{m}$$

Question 13

A basketball player runs with an initial velocity of $$6.0\ \mathrm{m/s}$$, accelerates at $$-2.0\ \mathrm{m/s^2$}$$ for $$6.0\ \mathrm{s}$$, and then continues at constant velocity. What is the player's velocity after $$12.0\ \mathrm{s}$$?

Accepted Answer

$$-6.0\ \mathrm{m/s}$$

Question 14

A car starts from rest and accelerates at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$10.0\ \mathrm{m/s}$$

Question 15

A ball rolls up a ramp and then back down. The acceleration along the ramp is constant and negative. Which of the following is true?

Accepted Answer

The velocity decreases as the ball rolls up and increases (in the negative direction) as it rolls down.

Question 16

A car travels with a velocity given by $$v(t) = 3t^2$ (in m/s). What is the displacement between t = 0$ and t = 2$$\ \mathrm{s}$$?

Accepted Answer

$$8\ \mathrm{m}$$

Question 17

A springbok accelerates at $$35\ \mathrm{m/s^2$}$$ over $$0.70\ \mathrm{m} as it $$leaps. What is its velocity as it leaves the ground?

Accepted Answer

$$7.0\ \mathrm{m/s}$$

Question 18

A car's acceleration is given by $$a(t) = 4\ \mathrm{m/s^2$}$$ for $$0 \u003c t \u003c 4\ \mathrm{s}$$ and $$a(t) = -2\ \mathrm{m/s^2$}$$ for $$4 \u003c t \u003c 8\ \mathrm{s}. If $$the initial velocity is $$10\ \mathrm{m/s}$$, what is the velocity at $$t = 8\ \mathrm{s}$$?

Accepted Answer

$$18\ \mathrm{m/s}$$

Kinematics in One Dimension: Position, Velocity, and Acceleration

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