Question

to pass a slow-moving truck, you want your fancy 1200 kg toyota corolla to accelerate from 26.8 m/s to 31.3 m/s from 60 mi/hr to 70 mi/hr]in 3 seconds. assume that the road is level, and that air resistance and friction can be ignored. what is the power required to do this?

Answer 1

The power required for a Toyota Corolla to accelerate from 26.8 m/s to 31.3 m/s in 3 seconds is 52.29 kW.

Step-by-step explanation:

Calculating the Power Required for Acceleration

To calculate the power required for a Toyota Corolla to accelerate from 26.8 m/s to 31.3 m/s in 3 seconds, we will use the formula:

Power = Force × Velocity

First, we calculate the force needed using Newton's second law (Force = mass × acceleration). The acceleration can be found by using the change in velocity over time (acceleration = (Δ velocity) / time).

Acceleration = (31.3 m/s - 26.8 m/s) / 3 s = 1.5 m/s²

Force = 1200 kg × 1.5 m/s² = 1800 N

The average velocity during this acceleration is (26.8 m/s + 31.3 m/s) / 2 = 29.05 m/s.

Thus, power = 1800 N × 29.05 m/s = 52290 W or 52.29 kW

This is the average power required during the 3-second acceleration period.