Question

The engine of a 1500-kg automobile has a power rat- ing of 75 kW. Determine the time required to accelerate this car from rest to a speed of 100 km/h at full power on a level road. Is your answer realistic

Answer 1

Answer:

7.72 seconds

The answer is not realistic as the time is very less to reach to a speed of 100 km/hr

also, we have not taken other factors into consideration like wind drag etc.

Explanation:

Data provided in the question:

Mass of the engine = 1500 kg

Power rating = 75 kW = 75,000 W

Initial speed, v₁ = 0

Final speed = 100 km/hr = $100\times\frac{5}{18}$ = 27.78 m/s

Now,

Power = Work done ÷ Time

also,

Work done = Final energy - Initial energy

= $\frac{1}{2}mv_2^2-\frac{1}{2}mv_1^2$

= $\frac{1}{2}\times1500\times27.78^2-\frac{1}{2}\times1500\times0^2$

= 578703.70 J

thus,

75,000 = 578703.70 ÷ time

or

time = 7.716 s ≈ 7.72 seconds

The answer is not realistic as the time is very less to reach to a speed of 100 km/hr

also, we have not taken other factors into consideration like wind drag etc.