The bus brakes at a constant acceleration of 1 m / s until it stops. Determine the braking distance

The bus brakes at a constant acceleration of 1 m / s until it stops. Determine the braking distance if its second half was covered in 5 seconds.

a = 1 m / s ^ 2.

t2 = 5 s.

S1 = S2 = S / 2.

S -?

Consider the move in the second half of S2.
Let us write down the definition for acceleration: a = (V – V02) / t2, where V = 0 is the final speed at the end of the second half, V02 is the speed at the beginning of movement in the second half, t2 is the time of movement in the second half.

a = V02 / t2.

V02 = a * t2.

Let’s write down the formula for determining the movement in the second half: S2 = (V ^ 2- V02 ^ 2) / 2 * a.
S2 = V02 ^ 2/2 * a = (a * t2) ^ 2/2 * a = a * t2 ^ 2/2.

Let us express the entire braking distance: S = 2 * S2 = a * t2 ^ 2.
S = 1 m / s ^ 2 * (5 s) ^ 2 = 25 m.

Answer: the braking distance of the bus was S = 25 m.