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.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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