Q: Which of the following is the correct expression for instantaneous velocity?

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

Question 1

Which of the following best describes the difference between kinematics and dynamics in physics?

Accepted Answer

Kinematics describes motion without regard to its causes, while dynamics describes motion with regard to its causes.

Question 2

A car moves along a straight road from $$x_1 = -5.0$$\ \mathrm{m}$$ to x_2$ = 2.0\ \mathrm{m}. $$What is the car's displacement?

Accepted Answer

$$7.0\ \mathrm{m}$$

Question 3

Which of the following statements about displacement in one-dimensional motion is correct?

Accepted Answer

Displacement can be positive or negative, but its magnitude is always positive.

Question 4

Given the position function $$x(t) = 4 - 27t + t^3$, what is the velocity function v(t$$)$$?

Accepted Answer

$$v(t) = -27 + 3t^2$

Question 5

Which equation gives the average velocity $$v_{ave}$$ over a time interval $$\Delta t$$?

Accepted Answer

$$v_{ave} = \frac{\Delta x}{\Delta t}$$

Question 6

A runner completes a 400 m lap in 50 s, ending at the starting point. What is the runner's average velocity?

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

A ball is tossed vertically upward with an initial velocity of $$12.0\ \mathrm{m/s}. $$What is the time to reach maximum height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$1.22\ \mathrm{s}$$

Question 9

Which kinematic equation is most appropriate to find the final velocity of an object under constant acceleration when displacement and initial velocity are known?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a$$\Delta x$$

Question 10

A car starts from rest and accelerates at $$1.5\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is its velocity at the end of this period?

Accepted Answer

$$7.5\ \mathrm{m/s}$$

Question 11

During free fall, what is the acceleration of an object at its highest point?

Accepted Answer

$$-9.8\ \mathrm{m/s^2$}$$

Question 12

If the velocity and acceleration of a particle have opposite signs, what happens to the speed of the particle?

Accepted Answer

The speed decreases.

Question 13

Which of the following is the correct unit for acceleration?

Accepted Answer

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

Question 14

A small mailbag is released from a helicopter that is descending steadily at $$1.50\ \mathrm{m/s}. $$After $$2.00\ \mathrm{s}$$, what is the speed of the mailbag (neglect air resistance)?

Accepted Answer

$$21.1\ \mathrm{m/s}$$

Question 15

Which of the following graphs best represents the velocity of an elevator cab that is initially stationary, then moves upward, and then stops?

Accepted Answer

A line that starts at zero, increases to a constant positive value, then returns to zero.

Question 16

Which of the following is the correct expression for the change in position $$\Delta x$$ under constant acceleration?

Accepted Answer

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

Question 17

A ball is thrown straight up. What is the sign of its displacement from the release point to the highest point?

Accepted Answer

Positive

Question 18

Which of the following integrals gives the change in velocity from $$t_0 to$$ $$t_1$$ when acceleration is a function of time?

Accepted Answer

$$v - v_0$ = \int_{t_0$}^{t_1$} a\, dt$$

Question 19

A car starts from rest and travels for $$5.0\ \mathrm{s}$$ with a uniform acceleration of $$1.5\ \mathrm{m/s^2$}. $$How far has the car gone?

Accepted Answer

$$18.75\ \mathrm{m}$$

Motion in One Dimension (Kinematics) – Study Notes

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