Question

(a) A runner starts from rest and in 3 s reaches a speed of 8 m/s. If we assume that the speed changed at a constant rate (constant net force), what was the average speed during this 3 s interval?

Answer 1

During the 3 s interval, the average velocity was 4 m/s.

Step-by-step explanation:

Hi there!

The average velocity (AV) is calculated as follows:

AV = Δx / Δt

Where:

Δx = traveled distance.

Δt = elapsed time.

The traveled distance (x) is calculated as follows:

x = x0 + v0 · t + 1/2 · a · t²

Where:

x0 = initial position.

v0 = initial velocity.

t = time.

a = acceleration.

Since x0 and v0 are equal to zero, the equation gets reduced to:

x = 1/2 · a · t²

Since the acceleration is constant, it can be calculated with this equation:

a = v/t

a = 8 m/s / 3 s

a = 8/3 m/s²

Then, the traveled distance will be:

x = 1/2 · a · t²

x = 1/2 · 8/3 m/s² · (3 s)²

x = 12 m

And the average velocity will be:

AV = Δx / Δt

AV = 12 m / 3 s = 4 m/s

During the 3 s interval, the average velocity was 4 m/s.