Q: Which equation correctly defines instantaneous velocity?

$$v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$$

Question 1

A car moves from $$x_1 = 10$$\ \mathrm{m}$$ to x_2$ = 6\ \mathrm{m} in$$ $$t_1 = 5$$\ \mathrm{s}$$ to t_2$ = 7\ \mathrm{s}. $$What is the car's average velocity during this interval?

Accepted Answer

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

Question 2

Which of the following statements about displacement is correct?

Accepted Answer

Displacement is a vector defined as $$\Delta x = x_2$ - x_1$.

Question 3

A runner moves from $$x_1 = 0$$\ \mathrm{m}$$ to x_2$ = 20\ \mathrm{m} in$$ $$t_1 = 0$$\ \mathrm{s}$$ to t_2$ = 4\ \mathrm{s}. $$What is the runner's average speed?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 4

Which of the following best describes the difference between average velocity and average speed?

Accepted Answer

Average velocity can be negative, while average speed is always positive.

Question 5

If a car travels leftward from $$x_1 = 10$$\ \mathrm{m}$$ to x_2$ = 6\ \mathrm{m}$$, what is the direction of its displacement?

Accepted Answer

Leftward

Question 6

Which equation correctly defines instantaneous velocity?

Accepted Answer

$$v = \lim_{\Delta t 	o 0} \frac{\Delta x}{\Delta t}$$

Question 7

A ball is thrown straight up with an initial velocity of $$v_0 = 10$$\ \mathrm{m/s}$$. Neglecting air resistance, what is its velocity at the highest point?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 8

Which of the following is a necessary assumption for using the standard kinematic equations?

Accepted Answer

Acceleration must be constant.

Question 9

A car accelerates uniformly from rest ($$v_0 = 0$) at a = 2$$\ \mathrm{$$m/s^2$$}$$ for t = 5$$\ \mathrm{s}$$. What is its final velocity?

Accepted Answer

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

Question 10

Which of the following is the correct formula for displacement under constant acceleration?

Accepted Answer

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

Question 11

A train moves with a constant velocity of $$v = 15\ \mathrm{m/s}$$ for $$t = 8\ \mathrm{s}. $$What is its displacement?

Accepted Answer

$$120\ \mathrm{m}$$

Question 12

Which of the following is true about reference frames in 1D kinematics?

Accepted Answer

Reference frames can be moving.

Question 13

A car backs up from $$x_1 = 10$$\ \mathrm{m}$$ to x_2$ = 6\ \mathrm{m} in$$ $$2\ \mathrm{s}. $$What is its average velocity?

Accepted Answer

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

Question 14

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 15

A car starts at $$x_0 = 0$$\ \mathrm{m}$$ with v_0$ = 5\ \mathrm{m/s}$$ and accelerates at $$a = 3\ \mathrm{m/s^2$}$$ for $$t = 4\ \mathrm{s}. $$What is its final position?

Accepted Answer

$$44\ \mathrm{m}$$

Question 16

Which of the following is the correct definition of acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t}$$

Question 17

A ball is dropped from rest and falls under gravity ($$g = 10\ \mathrm{m/s^2$}). $$What is its velocity after $$3\ \mathrm{s}$$?

Accepted Answer

$$30\ \mathrm{m/s}$$

Question 18

Which of the following is NOT a fundamental variable in 1D kinematics?

Accepted Answer

Mass

Question 19

A car moves with a constant acceleration of $$a = 2\ \mathrm{m/s^2$}$$, starting from $$v_0 = 4$$\ \mathrm{m/s}$$. What is its velocity after t = 3$$\ \mathrm{s}$$?

Accepted Answer

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

Question 20

Which of the following is the correct formula for average velocity when acceleration is constant?

Accepted Answer

$$\bar{v} = \frac{v_0$ + v}{2}$$

Chapter 2 - Kinematics in One Dimension (1D): Models, Variables, and Equations

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