Question

How long (in s) will it take an 870 kg car with a useful power output of 38.0 hp (1 hp = 746 w) to reach a speed of 11.0 m/s, neglecting friction? (assume the car starts from rest.)

Answer 1

Using the work-energy principle, it will take approximately 1.86 seconds for an 870 kg car with a power output of 38.0 hp to reach a speed of 11.0 m/s, neglecting friction.

Step-by-step explanation:

To determine how long it will take an 870 kg car with a power output of 38.0 hp to reach a speed of 11.0 m/s, starting from rest and neglecting friction, we can use the work-energy principle. The work done by the car's engine will be converted into the car's kinetic energy.

First, convert horsepower to watts:
38 hp × 746 W/hp = 28,348 W.

Since kinetic energy (KE) = 0.5 × mass × velocity^2, the kinetic energy at 11.0 m/s is:
KE = 0.5 × 870 kg × (11.0 m/s)^2 = 52,695 J.

Power is the rate at which work is done, so time can be calculated as:
Time = Work / Power = KE / Power Output.

Time = 52,695 J / 28,348 W ≈ 1.86 s.

So, it will take approximately 1.86 seconds for the car to reach a speed of 11.0 m/s.