A car starts from rest and accelerates uniformly for 8.0 s, reaching a final speed of 16 m/s. We need to find the acceleration of the car, the average velocity of the car, and the distance traveled by the car.

1. Problem Description

A car starts from rest and accelerates uniformly for 8.0 s, reaching a final speed of 16 m/s. We need to find the acceleration of the car, the average velocity of the car, and the distance traveled by the car.

2. Solution Steps

a. Finding the acceleration:

The acceleration $a$ is the change in velocity divided by the time taken. Since the car starts from rest, the initial velocity $v_i = 0$ m/s. The final velocity is $v_f = 16$ m/s, and the time is $t = 8.0$ s.

$a = \frac{v_f - v_i}{t}$

$a = \frac{16 - 0}{8}$

$a = 2$ m/s$^2$

b. Finding the average velocity:

Since the acceleration is uniform, the average velocity $v_{avg}$ can be calculated as the average of the initial and final velocities.

$v_{avg} = \frac{v_i + v_f}{2}$

$v_{avg} = \frac{0 + 16}{2}$

$v_{avg} = 8$ m/s

c. Finding the distance traveled:

The distance $d$ can be calculated using the average velocity and the time.

$d = v_{avg} \times t$

$d = 8 \times 8$

$d = 64$ m

Alternatively, the distance $d$ can be calculated using the following kinematic equation:

$d = v_i t + \frac{1}{2} a t^2$

$d = 0 \times 8 + \frac{1}{2} \times 2 \times 8^2$

$d = 0 + 1 \times 64$

$d = 64$ m

3. Final Answer

a. The acceleration of the car is 2 m/s$^2$.

b. The average velocity of the car is 8 m/s.

c. The distance traveled by the car is 64 m.