Q: Which of the following is the correct definition of instantaneous acceleration?

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

Question 1

A car travels 100 m east, then 150 m west along a straight road. What is the car's displacement from its starting point?

Accepted Answer

$$50\ \mathrm{m}$$\ west

Question 2

Which of the following statements about displacement and distance travelled is correct?

Accepted Answer

Displacement is a vector, and distance travelled is a scalar.

Question 3

A runner completes a lap around a 400 m track, ending at the starting point after 80 s. What is the runner's average velocity?

Accepted Answer

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

Question 4

Given the position function $$x(t) = 2 + 3t^2$, what is the instantaneous velocity at t = 4$$\ \mathrm{s}$$?

Accepted Answer

$$v = 24\ \mathrm{m/s}$$

Question 5

A cyclist moves along a straight path with a velocity given by $$v(t) = 5 + 2t. $$What is the cyclist's acceleration?

Accepted Answer

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

Question 6

A car accelerates from rest at $$3\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = 15\ \mathrm{m/s}$$

Question 7

Which equation gives the position $$x of an $$object under constant acceleration, starting from initial position $$x_0$$ and initial velocity $$v_0$$?

Accepted Answer

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

Question 8

A ball is thrown vertically upward with an initial velocity of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is its velocity after $$2\ \mathrm{s}$$? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$v = -9.6\ \mathrm{m/s}$$

Question 9

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

Accepted Answer

$$a_{ave} = \frac{v_2$ - v_1$}{t_2$ - t_1$}$$

Question 10

A solar-powered car accelerates from rest to $$60\ \mathrm{km/h} in$$ $$10\ \mathrm{s}. $$What is its average acceleration in $$\mathrm{m/s^2$}$$?

Accepted Answer

$$a_{ave} = 1.67\ \mathrm{m/s^2$}$$

Question 11

If $$x(t) = 5 + 4t + 3t^2$, what is the instantaneous acceleration at t = 2$$\ \mathrm{s}$$?

Accepted Answer

$$a = 6\ \mathrm{m/s^2$}$$

Question 12

A train moves with constant acceleration. If its initial velocity is $$2\ \mathrm{m/s}$$ and after $$6\ \mathrm{s}$$ its velocity is $$14\ \mathrm{m/s}$$, what is its acceleration?

Accepted Answer

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

Question 13

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

Accepted Answer

$$x = x_0$ + v_0$ t^2$

Question 14

A car travels 200 m east at $$5\ \mathrm{m/s}$$, then 280 m west at $$4\ \mathrm{m/s}. $$What is the car's average speed for the entire trip?

Accepted Answer

$$4.4\ \mathrm{m/s}$$

Question 15

Which physical quantity is represented by the slope of the tangent to a position vs. time graph?

Accepted Answer

Instantaneous velocity

Question 16

An antelope moves with constant acceleration, covering $$70.0\ \mathrm{m} in$$ $$7.00\ \mathrm{s}. $$Its speed at the end is $$15.0\ \mathrm{m/s}. $$What was its speed at the start?

Accepted Answer

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

Question 17

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

Accepted Answer

Average velocity equals instantaneous velocity.

Question 18

A ball is dropped from rest and falls freely under gravity. Which equation gives its velocity after time $$t$$?

Accepted Answer

$$v = v_0$ + at$$

Question 19

Which of the following is the correct definition of instantaneous acceleration?

Accepted Answer

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

Kinematics in One Dimension: Position, Velocity, and Acceleration

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