The car has an initial speed of 10m/s when the traffic light turns red and starts to decelerate at -5 m/s². How far does the car travel before it stops?

Let the velocity, distance and time to be v, s and t respectively. The velocity at 0 and t second is represented by v₀ and v_t respectively.

In order to find the traveling distance, the time spent on stopping the car should to be calculated first. The velocity function is

     v_t = v₀ + at

in which v₀ = 10, v_t = 0 and a = -5. Substituting v₀, v₀ and a into the above equation gives

     t = 2.0

The stopping distance is the integral of velocity with respect to time, that is

In the above equation, the lower limit is the time that the car starts to brake, which is 0 seconds. The upper limit is the time that the car stops, which is 2 seconds.The Fundamental Theorem of Calculus gives

     

The distance the car travels can be calculated

The braking distance for different intervals can be calculated by changing the upper and lower limit of the integral. For example, the braking distance between 0.5 to 1.5 seconds in the above case is