The body moves under the action of a constant force of 2 N according to the law S = 6t + 4t ^ 2.

The body moves under the action of a constant force of 2 N according to the law S = 6t + 4t ^ 2. The direction of the force is the same as the direction of movement. Determine the average power in the time interval t1 = 3s to t2 = 5s.

Given:

F = 2 Newtons – the force under which the body moves;

S = 6 * t + 4 * t ^ 2 – the equation of body motion;

t1 = 3 seconds;

t2 = 5 seconds.

It is required to determine N (Watt) – power in the time interval from t1 to t2.

Let’s find the distance that the body has traveled in a given period of time:

L = S2 – S1 = 6 * t2 + 4 * t2 ^ 2 – 6 * t1 – 4 * t12 = 6 * 5 + 4 * 5 ^ 2 – 6 * 3 – 4 * 32 = 30 + 100 – 18 – 45 = 67 meters.

Then the work of force for this period of time will be equal to:

A = F * L = 2 * 67 = 134 Joules.

The power will be equal to:

N = A / (t2 – t1) = 134 / (5 – 3) = 134/2 = 67 watts.

Answer: the power is 67 watts.