# Power of a car, time distance speed mass

1. Jul 13, 2009

### abruski

1. The problem statement, all variables and given/known data

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)
2. Relevant equations

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

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

$$P = Fv$$

$$F = ma$$

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

$$A = Fs$$

$$s = vt$$

3. 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.

2. Jul 13, 2009

### Staff: Mentor

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

3. Jul 13, 2009

### 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

4. Jul 13, 2009

### Staff: Mentor

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.

5. Jul 13, 2009

### abruski

how come distance is not 100m?

6. Jul 13, 2009

### Staff: Mentor

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

7. Jul 13, 2009

### abruski

What about the acceleration?

8. Jul 13, 2009

### Staff: Mentor

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.