Question

A child is playing with a remote-controlled car. What is the net power needed to change the speed of the 2 kg toy car from 0.2 m/s to 0.5 m/s in 3 seconds?

a) 0.07 W
b) 0.25 W
c) 0.08 W
d) 0.10 W

Answer 1

The net power needed to change the speed of a 2 kg toy car from 0.2 m/s to 0.5 m/s in 3 seconds is 0.07 watts.

Step-by-step explanation:

To calculate the net power needed to change the speed of the toy car, we can use the work-energy principle and the definition of power. Power is the rate at which work is done, and work is related to the kinetic energy change ΔKE of the car. The kinetic energy change when the car accelerates is given by ΔKE = 0.5 * m * (v_f^2 - v_i^2), where m is the mass of the car, v_f is the final velocity, and v_i is the initial velocity. For the given velocities of 0.5 m/s and 0.2 m/s and a mass of 2 kg, we get ΔKE = 0.5 * 2 kg * (0.5^2 - 0.2^2) J = 0.5 * 2 * (0.25 - 0.04) J = 0.5 * 2 * 0.21 J = 0.21 J. The power needed is the work done divided by the time, so P = ΔKE / t, where t is the duration of 3 seconds. Thus, P = 0.21 J / 3 s = 0.07 W.