Question

A 2000 kg car accelerates from 0 to 25 m / s in 21.0 s. How much is the average power delivered by the motor? (1 hp = 746 W)

Answer 1

Answer: 40.2 hp

Explanation:

The mass of the car is 2000kg.

in 21 seconds, it accelerates from 0m/s to 25m/s, so the average acceleration is:

a = (25m/s)/(21s) = 1.2 m/s^2

We know that force = mass*acceleration, then:

F = 2000kg*1.2m/s^2 = 2400N.

Now, the Power can be written as:

P = W/t where W is work = F*d (force per distance) and t is time.

then we have:

P = (F*d)/t and d/t  is the average velocity, and we know the velocity v = 25m/s, so the average velocity will be (1/2)*25m/s = 12.5m/s

P = F*12.5m/s

and the force is F = 2400N

P = 2400 N*12.5m/s = 30,000 W

and we know that 1hp = 746 W

then, P = (30,000/746) hp = 40.2 hp

Answer 2

Answer:

$P=40hp$

Explanation:

Hello,

In this cased, for the given velocities, we can compute the work done by the car as shown below, considering the kinetic energy only:

$W=\frac{1}{2}m(v_f^2-v_0^2)$

Whereas the mass is 2000 kg, the final velocity is 25 m/s and the initial velocity is 0 m/s, therefore the work is:

$W=\frac{1}{2}*2000kg*[(25\frac{m}{s})^2 -(0\frac{m}{s})^2]\\\\W=\frac{1}{2}*2000kg*625\frac{m^2}{s^2} \\\\W=6.25x10^5J$

Now, the power:

$P=\frac{W}{t}=\frac{6.25x10^5}{21.0s}=29762W$

And in horsepower:

$P=29762W*\frac{1hp}{746W} \\\\P=40hp$

Best regards.