Q: Which of the following is the correct mathematical definition of instantaneous velocity?

$$v_x = \lim_{\Delta t \to 0} \dfrac{\Delta x}{\Delta t}$$

Question 1

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

Accepted Answer

Distance is the total length of the path traveled, while displacement is the straight-line vector from the initial to the final position.

Question 2

A car moves along the x-axis from $$x_1 = 19$$\ \mathrm{m}$$ at t_1$ = 1.0\ \mathrm{s} to$$ $$x_2 = 277$$\ \mathrm{m}$$ at t_2$ = 4.0\ \mathrm{s}. $$What is the average velocity of the car?

Accepted Answer

$$v_{av-x} = \dfrac{277 - 19}{4.0 - 1.0} = 86\ \mathrm{m/s}$$

Question 3

A truck moves along the x-axis from $$x_1 = 277$$\ \mathrm{m}$$ at t_1$ = 16.0\ \mathrm{s} to$$ $$x_2 = 19$$\ \mathrm{m}$$ at t_2$ = 25.0\ \mathrm{s}. $$What is the sign of the displacement and the average velocity?

Accepted Answer

Displacement is negative, average velocity is negative.

Question 4

Which of the following best describes the instantaneous velocity at a specific time $$t$$?

Accepted Answer

The slope of the tangent line to the $$x vs$$ $$t$$ graph at that instant.

Question 5

Given the position function $$x(t) = 20 + 5.0 t^2$, what is the instantaneous velocity at t = 1.0$$\ \mathrm{s}$$?

Accepted Answer

$$v_x = 10\ \mathrm{m/s}$$

Question 6

A ball is thrown upward to a height of $$20\ \mathrm{m}$$ and caught after $$2\ \mathrm{s}. $$What is the displacement of the ball in $$2\ \mathrm{s}$$?

Accepted Answer

$$0\ \mathrm{m}$$

Question 7

Which of the following is true about speed and velocity?

Accepted Answer

Speed is the magnitude of velocity and is always positive.

Question 8

A particle moves from point A to point B along a curved path. Which statement is correct about the magnitude of its displacement?

Accepted Answer

It is smaller than the distance traveled.

Question 9

An object moves along a straight line. Its position as a function of time is shown in the graph. What is the displacement of the object from $$t = 0 to$$ $$t = 4\ \mathrm{s} if it $$starts at $$10\ \mathrm{m}$$ and ends at $$30\ \mathrm{m}$$?

Accepted Answer

$$20\ \mathrm{m}$$

Question 10

The $$x$$-$$t$$ graph of a particle's motion is shown. At which point is the velocity $$v_x$$ greatest (most positive)?

Accepted Answer

Point P

Question 11

The $$x$$-$$t$$ graph of a particle's motion is shown. At which point is the speed greatest?

Accepted Answer

Point S

Question 12

A particle moves along the $$x-$$axis with position $$x(t) = -4t + 2t^2$. What is the average velocity between t = 0$ and t = 2$$\ \mathrm{s}$$?

Accepted Answer

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

Question 13

A cat runs along the $$x-$$axis from point A to B to C. The distance from A to C is $$5.0\ \mathrm{m}$$, from B to C is $$10.0\ \mathrm{m}$$, time from A to B is $$20.0\ \mathrm{s}$$, and from B to C is $$8.0\ \mathrm{s}. $$What is the magnitude of its average velocity?

Accepted Answer

$$0.25\ \mathrm{m/s}$$

Question 14

Which of the following is the correct mathematical definition of instantaneous velocity?

Accepted Answer

$$v_x = \lim_{\Delta t 	o 0} \dfrac{\Delta x}{\Delta t}$$

Question 15

A motion diagram shows a particle's position at various instants with arrows representing velocity. What does a longer arrow indicate?

Accepted Answer

The particle is moving faster.

Question 16

If a car's position-time graph is a straight line with a positive slope, what can you conclude about its motion?

Accepted Answer

The car is moving with constant positive velocity.

Question 17

Which of the following is true about average speed and average velocity for a round-trip journey?

Accepted Answer

Average velocity is zero, but average speed is not zero.

Motion Along a Straight Line: Displacement, Velocity, and Speed

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