Question

A car of mass 1000 kg is moving with a constant speed of 20 m/s on a straight horizontal road with an output power of 20 kW. I f the output power is suddenly increased to 60 kW, what is the acceleration of thecar at this instant?

Answer 1

Question: A car of mass $1000\,\mathrm{kg}$ is moving with a constant speed of $20\,\mathrm{m/s}$ on a straight horizontal road with an output power of $20\,\mathrm{kW}$. If the output power is suddenly increased to $60\,\mathrm{kW}$, what is the acceleration of the car at this instant?

Solution:

$$P = \frac{A}{t} = \frac{F \cdot S}{t} = F \cdot V, \quad \text{where}$$ $$A = \text{work},$$ $$t = \text{time},$$ $$F = \text{force},$$ $$V = \text{speed}.$$ $$P_1 = 20000\,W, \quad V_1 = 20\,\frac{m}{s}$$ $$P_2 = 60000\,W$$

The first power is:

$$P_1 = F \cdot V_1$$ $$F = 1000\,N$$

The second speed:

$$V_2 = \frac{P_2}{F}$$ $$V_2 = \frac{60000}{1000} = 60\,\frac{m}{s}$$ $$\Delta P = \frac{\Delta A}{t}$$

Time is:

$$t = \frac{\Delta A}{\Delta P} = \frac{\frac{m \cdot (\Delta V)^2}{2}}{\Delta P} = 20\,\mathrm{s},$$

where

$$m = \text{mass of car},$$ $$\Delta V = (V_2 - V_1),$$ $$\Delta P = (P_2 - P_1).$$

ANSWER:

$$a = \frac{\Delta V}{t} = \frac{40}{20} = 2\,\mathrm{m/s^2}$$