Question

Consider a 2100-kg car cruising at a constant speed of 70 km/h. Now, the car starts to pass another car by accelerating to 110 km/h in 13 s. Determine the additional power needed to achieve this acceleration. What would your answer be if the total mass of the car were only 700 kg

Answer 1

`P=44.858kW`

For 700 kg:
`P=14.952kW`

Step-by-step explanation:

Power is given by the following formula:

`P=(W)/(\Delta t)`

Where W is the amount of work done during the time interval Δt.

Recall that work is equal to the change in kinetic energy:

`W=\Delta K\\W=K_2-K_1\\W=(mv_2^2)/(2)-(mv_1^2)/(2)`

`70(km)/(h)*(1000m)/(1km)*(1h)/(3600s)=19.44(m)/(s)\\110(km)/(h)*(1000m)/(1km)*(1h)/(3600s)=30.55(m)/(s)`

So, we have:

`P=(m)/(2\Delta t)(v_2^2-v_1^2)\\P=(2100kg)/(2*13s)((30.55(m)/(s))^2-(19.44(m)/(s))^2)=44858.33 W\\P=44.858kW`

For 700 kg:

`P=(700kg)/(2*13s)((30.55(m)/(s))^2-(19.44(m)/(s))^2)=14952.78 W\\P=14.952kW`