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

Answer:

$P=44.858kW$

For 700 kg: $P=14.952kW$

Explanation:

Power is given by the following formula:

$P=\frac{W}{\Delta t}$

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

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

$W=\Delta K\\W=K_2-K_1\\W=\frac{mv_2^2}{2}-\frac{mv_1^2}{2}$

$70\frac{km}{h}*\frac{1000m}{1km}*\frac{1h}{3600s}=19.44\frac{m}{s}\\110\frac{km}{h}*\frac{1000m}{1km}*\frac{1h}{3600s}=30.55\frac{m}{s}$

So, we have:

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

For 700 kg:

$P=\frac{700kg}{2*13s}((30.55\frac{m}{s})^2-(19.44\frac{m}{s})^2)=14952.78 W\\P=14.952kW$