A car has to be built to be able to accelerate from 0 to 60 kmph with 3 seconds. If the mass of the car is 1200 kg what is the work required by the engine to be done.
The mass of the car is 1200 kg. It has to be able to accelerate such that the speed of the car can reach 60 km/h from 0 km/h within 3 seconds.
Acceleration is the rate of change in velocity. If the initial speed is u and the final speed is v after time t, the acceleration is `a = (v - u)/t` . Convert the speed from km/h to m/s. 60 km/h = 60*1000/3600 = 50/3 m/s. To reach the required speed, the car has to accelerate at (50/3 - 0)/3 = 50/9 m/s^2.
If an object is accelerating at a m/s^2 and the initial velocity is u, the distance traveled in time t is s = u*t + (1/2)*a*t^2
Here, the car accelerates at 50/9 m/s^2, the distance traveled in 3 seconds is 0*3 + (1/2)*(50/9)*3^2 = 25 m
The force required to accelerate the car is 1200*(50/9) = 20000/3 and the work done is the product of force exerted and the displacement. This is equal to 500000/3 J
To increase the speed of the car from rest to 60 km/h in 3 seconds requires a work equal to 500000/3 J