If a 1000kg car accelerates from 0 to 60mph in 6 seconds, how many Watt-hours are used?

Question

If a 1000kg car accelerates from 0 to 60mph in 6 seconds, how many Watt-hours are used?

Answer 1

Use all metric units, so 60 mph equals approx. 100 kph (km/h) or 100/3.6 = 27.78 m/s.

The work (energy) used to produce the acceleration of the car is

E = F*s, where

F - inertial force opposing acceleration, s - distance traveled until the 60 mph is reached, * is multiplication.

Acceleration: a = v/t = 27.78/6 = 4.63 m/s2

(uniform acceleration is assumed)

Inertial force: F = m*a = 1000 * 4.63 = 4629.63 N (newton, force unit)

Distance during acceleration: s = v^2/2a = 27.78^2/(2*4.63) = 83.34 m

(^2 means square, or v*v)

Work (energy) is

E = F * s = 4629.63 * 83.34 = 385,833.36 Nm (=Ws, watt-seconds)

To convert the result into watt-hours, divide by 3600:

E = 385,833.36/3600 = 107.18 Wh (watt-hours)

which is your answer.