Question

A 120 kg car accelerates from initial speed 5.0 m/s to final speed 10.0 m/s in 5.0 seconds. How much power (watts) does that require?

Answer 1

In order to determine the required power, use the following formula:

`P=(W)/(t)`

where

t: time = 5.0 s

W: work

calculate the work W as follow:

`W=F\cdot d=m\cdot a\cdot d`

where

m: mass = 120 kg

a: acceleration = ?

d: distance

calculate the acceleration as follow:

`a=(v-v_0)/(t)=\frac{10.0\text{ m/s- 5.0m/s}}{5.0s}=1(m)/(s^2)`

the distance can be obtained by using the following formula:

`d=v_0\cdot t+(1)/(2)at^2=((5.0m)/(s))(5.0s)+(1)/(2)((1m)/(s^2))(5.0s)^2=37.5m`

then, replace the previous values of a and d to calculate W:

`W=(120kg)((1m)/(s^2))(37.5m)=4500J`

Finally, replace W and d into the formual for the power P:

`P=(4500J)/(5.0s)=900W`

Hence, 900 watts are required to accelerate the car.