Question

A 900-kg car cruising at a constant speed of 60 km/h is to accelerate to 100 km/h in 4 s. The additional power needed to achieve this acceleration is (a) 56 kW (b) 222 kW (c) 2.5 kW (d) 62 kW (e) 90 kW

Answer 1

To solve this problem we will apply the concepts related to power as a function of the change of energy with respect to time. But we will consider the energy in the body equivalent to kinetic energy. The change in said energy will be the difference between the two velocity data given by half of the mass. We will first convert the given units into an international system like this

Initial Velocity,

$V_i = 60km/h (\frac{1000m}{1km})(\frac{1h}{3600s})$

$V_i = 16.6667m/s$

Final Velocity,

$V_f = 100km/h (\frac{1000m}{1km})(\frac{1h}{3600s})$

$V_f = 27.7778m/s$

Now Power is defined as the change of Energy over the time,

$P = \frac{E}{t}$

But Energy is equal to Kinetic Energy,

$P = \frac{\frac{1}{2} m\Delta v^2}{t}$

$P = \frac{\frac{1}{2} m(v_f^2-v_i^2)}{t}$

Replacing,

$P = \frac{\frac{1}{2} (900)(27.7778^2-16.6667^2)}{4}$

$P = 56kW$

Therefore the correct answer is A.