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

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.

Step-by-step 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*(5)/(18)` = 27.78 m/s

Now,

Power = Work done ÷ Time

also,

Work done = Final energy - Initial energy

=
`(1)/(2)mv_2^2-(1)/(2)mv_1^2`

=
`(1)/(2)*1500*27.78^2-(1)/(2)*1500*0^2`

= 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.