Let the car will overtake the truck after time 't'. In this time, the distance cover by the car is equal to the distance cover by the truck.
Distance cover by the truck in time 't' = Speed of the truck× time = 25t m
Distance cover by the car can be calculated using the second equation of motion, that is
[tex] s= ut + \frac{1}{2}at^{2} [/tex]
As, the car started from the rest its initial velocity is zero.
Acceleration of the car= 3 m/s²
∴ Distance cover by the car = 0×t + [tex] \frac{1}{2}*3*t^{2} [/tex]
= [tex] \frac{3}{2}t^{2} [/tex] m
Equating the distances cover by the car and the truck, we get
[tex] 25t=\frac{3}{2}t^{2} [/tex]
t=[tex] \frac{50}{3} [/tex] = 16.66 s
Hence, the car will overtake the truck in 16.66 s.
