Question

The engine of a car applies enough force to accelerate the car from 0 km/h to 180 km/h covering a distance of 100 m. If the mass of the car is 3 tons. Find the force applied by the car's engine?

Answer 1

Force = Mass x Acceleration
Mass = 3 ton
Final Velocity = 180 Kmph = 50 m/s. = V
Distance travelled while acclerating to the Final velocity from rest = 100 meter = S
Acceleration = V^2/(2*S) = 2500/(200) = 12.5 [m/(s^2)] { Assuming accleration happened linearly } ie., car accelerated
to final speed in 4 seconds at the rate of 12.5 m/s increase in velocity every second.

Force = 3000 * 12.5 = 37500 N = 37.5 KN ( Kilo Newton ).

Answer 2

Let us write the following equations:
Vf = Vi + a t (1)
D = Vi t + 1/2 a t ^2 (2)
Since Vi = 0 we can rewrite (1) and (2) as follows
Vf = a t (1)
D = 1/2 a t^2 (2)
Then,
D = 1/2 x Vf x t Therefore 100 m = 1/2 x 180000/3600 x t It yields t = 4 seconds
By replacing 4 seconds in equation (1)
a = (180000/3600) / 4 = 12,5 m/sec^2
Finally, F = m x a
F = 3000 Kgs x 12,5 m/sec^2 = 37500 Newtons