Question

A bus of mass $1000$ kg has an engine which produces a constant power of $50$ kW. If the resistance to motion, assumed constant is $1000$N. The maximum speed at which the bus can travel on level road and the acceleration when it is travelling at $25$ m/s, will respectively be?

• A. $50$ m/s, $1.0$ $m/s^2$
• B. $1.0$ m/s, $50$ $m/s^2$
• C. $5.0$ m/s, $10$ $m/s^2$
• D. $10$ m/s, $5$ $m/s^2$

Answer 1

The correct option is A $50$ m/s, $1.0$ $m/s^2$

Given mass=1000 kg; power=50 KW; Force(F)=1000 N and initial velocity=25 m/s

We know Force=mass$\times$acceleration

a$=\frac{1000}{1000}=1m/s^2$

Also power=$\frac{workdone}{Time}=\frac{F\times s}{t}$

Now multiplying bith numerator and denomerator with time we get,

$=\frac{F\times s\times t}{t\times t}=Fat$

as acceleration = $\frac{m}{s^2}$

Thus time t$=\frac{50\times {10}^3}{{10}^3\times 1}=50\text{s}$

as we know,

s=ut+$\frac{1}{2}a{t}^2$

s=25(50)+$\frac{{50}^2}{2}$=2500 m

Now velocity$=\frac{\text{Distance covered}}{\text{time}}$

v$=\frac{2500}{50}=50m/s$