Answer:
The average speed of the runner is 4 m/s.
Explanation:
Hi there!
The average speed (a.s) is calculated by dividing the traveled distance (d) over the time needed to travel that distance (t):
a.s = d / t
So, let´s find the distance traveled in those 3 s. For that, we can use the equation of position of an object moving in a straight line with constant acceleration:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x = position of the object at time t.
x0 = initial position.
v0 = initial velocity.
t = time.
a = acceleration.
If we place the origin of the frame of reference at the point where the runner starts, then, x0 = 0. Since the runner starts from rest, v0 = 0. So, the equation gets reduced to this:
x = 1/2 · a · t²
We have the time (3 s), so let´s find the acceleration. For that, we can use the equation of velocity of an object moving in a straight line with constant acceleration:
v = v0 + a · t
Where "v" is the velocity at a time "t". Since v0 = 0, then:
v = a · t
At t = 3 s, v = 8 m/s
8 m/s = a · 3 s
8/3 m/s² = a
So let´s find the position of the runner at t = 3 s (In this case, the position of the runner will be equal to the traveled distance):
x = 1/2 · a · t²
x = 1/2 · 8/3 m/s² · (3 s)²
x = 12 m
Now, we can calcualte the average speed:
a.s = d/t
a.s = 12 m / 3 s
a.s = 4 m/s
The average speed of the runner is 4 m/s.
