Question

A 2000 kg car, initially at rest, is accelerated along a horizontal roadway at 3 m/s2. What is the average power required to bring the car to a final speed of 20 m/s?

Answer 1

To find the average power required to bring the car to a final speed of 20 m/s, we need to calculate the force on the car using Newton's second law. Then, we can use the equation Power = Force × Velocity to find the average power.

Step-by-step explanation:

To find the average power required to bring the car to a final speed of 20 m/s, we can use the equation:

Power = Force × Velocity

First, we need to find the force on the car. We can use Newton's second law, which states that force is equal to mass times acceleration:

Force = mass × acceleration

Given that the mass of the car is 2000 kg and the acceleration is 3 m/s², we can calculate the force:

Force = 2000 kg × 3 m/s² = 6000 N

Now we have the force and the velocity (20 m/s), so we can calculate the power:

Power = 6000 N × 20 m/s = 120,000 watts

Therefore, the average power required to bring the car to a final speed of 20 m/s is 120,000 watts.

Answer 2

`6*10^4 W`

Step-by-step explanation:

We know

`P= W/t\\`

Where P is power, W is work, and t is time.

We can calculate work since we have all its values, but we need to find t. We do this with kinematics.

`v_f=v_i+at\\20=3t\\t=20/3 s`

All values were taken from the text, where final velocity is 20, initial velocity is 0, and acceleration is 3.

We now just replace. Note that work in this case will only be change in kinetic energy since we don't have any potential energy.

`P=W/t\\P=[delta]K.E./t\\\\P=((1/2)mv_f^2-0)/(20/3)\\P=60 000 W`

Using scientific notation:

`P = 6*10^4 W`

Where W in this case is Watts

I hope this helped :)