Question

An 8 kg block slides on a horizontal, rough surface with a constant acceleration. If during a 5 second interval, its kinetic energy decreased from 70 J to 40 J, what was its average speed during the interval?

Answer 1

The average speed of the block during the interval is -0.4 m/s.

Step-by-step explanation:

The average speed of the block during the interval can be found by calculating the change in distance over the change in time. We can use the equation:

Average speed = (Change in distance) / (Change in time)

We are given the change in kinetic energy of the block, so we can use the work-energy principle to find the change in distance:

Change in kinetic energy = Work done on the block

Since the block slides on a rough surface, the work done on the block is done against the force of friction. Therefore, we can write:

Work done on the block = Force of friction * Change in distance

By substituting these equations and given values, we can solve for the change in distance and then use it to calculate the average speed:

Change in kinetic energy = 40 J - 70 J = -30 J
Work done on the block = Force of friction * Change in distance

-30 J = Force of friction * Change in distance

Force of friction = 15 N (given)

-30 J = 15 N * Change in distance

Change in distance = -30 J / 15 N = -2 m

Average speed = (Change in distance) / (Change in time) = (-2 m) / (5 s) = -0.4 m/s