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:

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

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:

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

the distance can be obtained by using the following formula:

$d=v_0\cdot t+\frac{1}{2}at^2=(\frac{5.0m}{s})(5.0s)+\frac{1}{2}(\frac{1m}{s^2})(5.0s)^2=37.5m$

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

$W=(120kg)(\frac{1m}{s^2})(37.5m)=4500J$

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

$P=\frac{4500J}{5.0s}=900W$

Hence, 900 watts are required to accelerate the car.