Two buses depart from the stop simultaneously in the same direction. If the acceleration of one is 1.0 m / s ^ 2

Two buses depart from the stop simultaneously in the same direction. If the acceleration of one is 1.0 m / s ^ 2, and the second is 1.5 m / s ^ 2, then the distance of 100 m will be between them after a time equal to?

V0 = 0 m / s.

a1 = 1 m / s2.

a2 = 1.5 m / s2.

S = 100 m.

t -?

With uniformly accelerated movement, the path S traversed by the bus will be expressed by the formula: S = V0 * t + a * t ^ 2/2, where V0 is the initial speed, t is the time the bus travels, and a is the acceleration during movement.

Since the buses begin to move from a state of rest V0 = 0 m / s, the formula will take the form: S = a * t ^ 2/2.

Let us express the path traveled by the first and second buses: S1 = a1 * t ^ 2/2, S2 = a2 * t ^ 2/2.

S2 – S1 = S.

a ^ 2 * t ^ 2/2 – a1 * t ^ 2/2 = S.

(a2 – a1) * t ^ 2 = 2 * S.

t = √ (2 * S / (a2 – a1)).

t = √ (2 * 100 m / (1.5 m / s2 – 1 m / s2)) = 20 s.

Answer: between buses the distance S = 100 m will be in time t = 20 s.