Power of a car, time distance speed mass

[abruski]

Homework Statement

A car with mass m = 1 metric ton (1000 kg) in time t = 5 seconds reaches speed v = 20 m/s

What is the power of the car? P = ? kW (kilo Watts)

Homework Equations

F - force, a - acceleration, A - work, s - distance

$$P = \frac{A}{t}$$

$$P = Fv$$

$$F = ma$$

$$a = \frac{v}{t}$$

$$A = Fs$$

$$s = vt$$

The Attempt at a Solution

The answer given in the book is 40 kW but I get 80 kW. With the 40 kW I get that the acceleration s 2 m/s$$^{2}$$, which means that
$$\frac{v}{t} = \frac{20}{5} = 2$$

??

Maybe I miss something. Any help is appreciated.

 

[Doc Al]

The answer given in the book is 40 kW but I get 80 kW.

Show how you got your answer. Hint: Find the average power.

 

[abruski]

$$a = \frac{v}{t} = \frac{20}{5} = 4 \frac{m}{s^{2}}$$

$$s = vt = 100 m$$

$$F = ma = 1000*4 = 4000 N$$

$$A = Fs = 4000*100 = 400000 J$$


$$P = Fv = 4000*20 = 80 000 W$$

$$P = \frac{A}{t} = \frac{400000}{5} = 80 000 W$$

seems pretty straightforward to me

 

[Borek]

40 kW is a correct answer.

Distance is not 100 m.

While the final answer should be identical no matter how you solve the question, comparing final energy of the car with the work done seems to be much easier approach.

 

[abruski]

how come distance is not 100m?

 

[Borek]

20 m/s is a FINAL speed, not average.

 

[abruski]

What about the acceleration?

 

[Doc Al]

What about the acceleration?

What about it? Realize that the instantaneous power varies throughout the motion. You want the average power. Rather than mess around with kinematics, use the most basic definition of power as energy/time.