a car starting from rest accelerates at the rate f through a dist s, then continues at constant speed - Physics - Motion In A Straight Line

Question

a car starting from rest accelerates at the rate f through a
dist s, then continues at constant speed for some time and then
decelerates at the rate of f/2to come to rest if the total dist is
5s , then prove that s=ft2/2

Somnath physics · Accepted Answer

Let the time moved by the car at constant speed be t

Distance moved with acceleration f = s

Total distance moved = 5s

Let v = velocity of the car it reached after moving with
acceleration f for a distance s

a car starting from rest accelerates at the rate f through a dist. s, then continues at constant speed for some time and then decelerates at the rate of f/2to come to rest. if the total dist. is 5s., then prove that s=ft2/2

a car starting from rest accelerates at the rate f through a dist. s, then continues at constant speed for some time and then decelerates at the rate of f/2to come to rest. if the total dist. is 5s., then prove that s=ft²/2