$$a = \frac{v - v_0$}{t} = \frac{40.0\ \text{m/s} - 0}{8.4\ \text{s}} = 4.76\ \text{m/s}^2$$

$$x = 0 + 0 \times 8.4 + \frac{1}{2} \times 4.76 \times (8.4)^2$ = 167.6\ \text{m}$$

$$x = 0 + 10.0 \times 8.4 + \frac{1}{2} \times 4.76 \times (8.4)^2$ = 251.6\ \text{m}$$

$$x = \frac{1}{2} \times 2 \times 4.76 \times (8.4)^2$ = 335.2\ \text{m}$$

$$v = v_0$ + a t = 0 + 4.76 \times 8.4 = 40.0\ \text{m/s}$$

Question 1

A sports car starts at rest and accelerates uniformly to a speed of 40.0 m/s in 8.4 s. What is the car's acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{40.0\ 	ext{m/s} - 0}{8.4\ 	ext{s}} = 4.76\ 	ext{m/s}^2$$

Question 2

Using the kinematic equation $$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$, calculate the distance the car travels during the 8.4 s interval.

Accepted Answer

$$x = 0 + 0 	imes 8.4 + \frac{1}{2} 	imes 4.76 	imes (8.4)^2$ = 167.6\ 	ext{m}$$

Question 3

If the car had started with an initial velocity of 10.0 m/s instead of rest, what would be the total distance traveled in 8.4 s?

Accepted Answer

$$x = 0 + 10.0 	imes 8.4 + \frac{1}{2} 	imes 4.76 	imes (8.4)^2$ = 251.6\ 	ext{m}$$

Question 4

Which kinematic equation is most appropriate for finding the distance traveled by an object starting from rest and accelerating uniformly?

Accepted Answer

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

Question 5

A car accelerates uniformly from rest. After 8.4 s, its speed is 40.0 m/s. What is the average velocity during this interval?

Accepted Answer

$$v_{avg} = \frac{v_0$ + v}{2} = \frac{0 + 40.0}{2} = 20.0\ 	ext{m/s}$$

Question 6

If the acceleration of the car is doubled, how much distance will it cover in the same time interval (8.4 s)?

Accepted Answer

$$x = \frac{1}{2} 	imes 2 	imes 4.76 	imes (8.4)^2$ = 335.2\ 	ext{m}$$

Question 7

A car accelerates uniformly from rest to a speed $$v in $$time $$t. $$Which equation gives the distance traveled?

Accepted Answer

$$x = \frac{1}{2} v t$$

Question 8

If a car starts from rest and accelerates uniformly, which of the following statements is true about its velocity-time graph?

Accepted Answer

The graph is a straight line with a positive slope.

Question 9

A car starts from rest and accelerates uniformly. After 8.4 s, it covers 167.6 m. What is its final speed?

Accepted Answer

$$v = v_0$ + a t = 0 + 4.76 	imes 8.4 = 40.0\ 	ext{m/s}$$

Question 10

A car accelerates uniformly from rest. Which equation relates its final speed, acceleration, and distance traveled?

Accepted Answer

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

Kinematics: Calculating Distance Traveled During Uniform Acceleration

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