Calculate the power required to accelerate a 1150 kg car from rest to a final velocity of 30 m/s up a 100 m long uphill road with a slope of 30 degrees from horizontal over a time of 12 seconds. Disregard friction, air drag, and rolling resistance.

power required is 90.131 kW

Explanation:

Given data

mass of car (m) = 1150 kg

starting velocity (v1) = 0 m/s

final velocity (v2) = 30 m/s

slope angle = 30 degrees

slope distance = 100 m

to find out

power required

solution

we know the power = work / time

here time is given we have calculate the work

work is for car climb 100 m distance is total sum of potential energy + kinetic energy

and we know car climb 100m at 30 degree slope so vertical distance (h) will be h = 100 sin (30) = 50 m

so now potential energy = mass * gravity * height

potential energy = 1150 * 9.81 * 50 = 564075 J

kinetic energy = 1/2 * mass * velocity²

kinetic energy = 1/2 * 1150 * (v2 - v1) ²

kinetic energy = 1/2 * 1150 * (30 - 0) ² = 517500 J

now put all value in power formula

power = work / time

power = potential energy + kinetic energy / 12

power = 564075 + 517500 / 12 = 90131.25 W

power = 90.131 kW