To calculate the work required to accelerate a car, we need to consider the change in kinetic energy. The work done on an object is equal to the change in kinetic energy.
Given: Mass of the car (m) = 1300 kg Initial velocity (u) = 0 m/s (car is at rest) Final velocity (v) = 20 m/s Time taken (t) = 30 seconds Distance traveled (d) = 80 m
First, we can calculate the acceleration (a) using the kinematic equation:
v = u + at
20 = 0 + a * 30
a = 20 / 30 = 0.67 m/s²
Using the formula for work (W):
W = ΔKE = (1/2) * m * (v² - u²)
W = (1/2) * 1300 * (20² - 0²)
W = (1/2) * 1300 * 400
W = 260,000 Joules
Therefore, the work required to accelerate the 1300 kg car from rest to a velocity of 20 m/s in 30 seconds over a distance of 80 m is 260,000 Joules.