# a car starting from rest accelerates at the rate f through a distance s then continues at constant speed for same time t and then deccelerates at the rate f/2 to come to rest.If the totl distance is 5s then prove that s=1/2 f t^2

car starting from rest accelerates at the rate f through a distance s then continues at constant speed for same time t and then deccelerates at the rate f/2 to come to rest.If the totl distance is 5s then prove that s=1/2 f t^2

$total\ distance\\5s=s_{1-2}+s_{2-3}+s_{3-4}\\5s=s+ft^2+ft^2\\so, \ s=\frac{1}{2}ft^2$