A driver notices that her 1280 kg car slows down from 92 km/h to 68 km/h in about 7.5 s on the level when it is in neutral. Approximately what power (in watts) is needed to keep the car traveling at a constant 80 km/h

P = 25299.75 watts

Since 80km/h is the average speed of 92km/h and 68km/h, the power (in watts) is needed to keep the car traveling at a constant 80 km/h is P = 25299.75 watts

Explanation:

Given;

Mass of car m = 1280kg

initial speed v1 = 92km/h = 92*1000/3600 m/s = 25.56m/s

Final speed v2 = 68km/h = 68*1000/3600 m/s = 18.89m/s

time taken t = 7.5s

Change in the kinetic energy of the car within that period;

∆K. E = 1/2 * mv1^2 - 1/2 * mv2^2

∆K. E = 0.5m (v1^2 - v2^2)

Substituting the values, we have;

∆K. E = 0.5*1280 (25.56^2 - 18.89^2)

∆K. E = 189748.16J

Power used during this Change;

Power P = ∆K. E/t

Substituting the values;

P = 189748.16/7.5

P = 25299.75 watts

Since 80km/h is the average speed of 92km/h and 68km/h, the power (in watts) is needed to keep the car traveling at a constant 80 km/h is P = 25299.75 watts