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

$$a_x = \lim_{\Delta t \to 0} \frac{\Delta v_x}{\Delta t} = \frac{dv_x}{dt}$$

Question 1

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1 (in $$meters, with $$t in $$seconds). What is the instantaneous velocity of the car at $$t = 3 s$$?

Accepted Answer

$$v_x = 26 m/s$$

Question 2

A runner completes a 100 m dash in 10 s, starting from rest and accelerating uniformly for the first 4 s, then running at constant speed for the remaining time. What is the runner's average velocity?

Accepted Answer

$$v_{avg} = 10 m/s$$

Question 3

Which of the following statements about average speed and average velocity is correct for a car that drives 40 km east and then 40 km west in 2 hours?

Accepted Answer

The average speed is 40 km/h, but the average velocity is 0 km/h.

Question 4

A ball is thrown vertically upward with an initial velocity of $$v_0 = 20$ m/s. Neglecting air resistance, what is the velocity of the ball when it returns to its starting point?

Accepted Answer

$$-20 m/s$$

Question 5

A car accelerates from rest at a constant rate of $$2 m/s$^2. $$How far does it travel in the first 5 seconds?

Accepted Answer

$$50 m$$

Question 6

Which equation correctly relates the final velocity $$v_x$$, initial velocity $$v_{0x}$$, acceleration $$a_x$$, and displacement $$(x - x_0$)$$ for motion with constant acceleration?

Accepted Answer

$$v_x^2$ = v_{0x}^2 + 2a_x(x - x_0$)$$

Question 7

A stone is dropped from a height of 80 m. How long does it take to reach the ground? (Assume $$g = 9.8 m/s$^2$$ and neglect air resistance.)

Accepted Answer

$$4.04 s$$

Question 8

On a position-time ($$x$$-$$t) $$graph, what does the slope of the tangent at any point represent?

Accepted Answer

The instantaneous velocity at that point

Question 9

A car's velocity changes from $$10 m/s to$$ $$30 m/s in$$ $$4$$ seconds. What is its average acceleration?

Accepted Answer

$$2.5 m/s$^2$$

Question 10

A ball is thrown straight up with an initial velocity of $$15 m/s. $$What is its maximum height above the starting point? (Use $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$11.5 m$$

Question 11

Which of the following best describes the motion of a freely falling object (neglecting air resistance)?

Accepted Answer

It accelerates downward at a constant rate.

Question 12

A particle moves along the x-axis so that its velocity is given by $$v_x = 3t^2$ (in m/s, with t$ in seconds). What is the particle's acceleration at t = 2$ s?

Accepted Answer

$$a_x = 12 m/s$^2$$

Question 13

A car travels 60 km north in 1 hour, then 60 km south in 2 hours. What is the magnitude of its average velocity for the entire trip?

Accepted Answer

$$0 km/h$$

Question 14

If the acceleration of a particle is zero, which of the following must be true?

Accepted Answer

The velocity is constant.

Question 15

A car starts from rest and accelerates uniformly at $$a_x = 3 m/s$^2$$ for 6 seconds. What is its final velocity?

Accepted Answer

$$18 m/s$$

Question 16

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

Accepted Answer

$$a_x = \lim_{\Delta t 	o 0} \frac{\Delta v_x}{\Delta t} = \frac{dv_x}{dt}$$

Question 17

A car moves with a constant acceleration. Which of the following statements is true about its position-time graph?

Accepted Answer

It is a parabola.

Question 18

A ball is thrown downward from a height of 20 m with an initial speed of 5 m/s. How long does it take to hit the ground? (Use $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$1.53 s$$

Question 19

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

Accepted Answer

$$x = x_0$ + v$$_{0x}$$t + a_xt^3$

Motion Along a Straight Line: Kinematics and Dynamics

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