Determine how long it took the trolleybus, moving from a state of rest, on the path of 500m

Determine how long it took the trolleybus, moving from a state of rest, on the path of 500m, acquired a speed of 54 km / h. With what acceleration did he move?

V0 = 0 m / s.

S = 500 m.

V = 54 km / h = 15 m / s.

t -?

a -?

We will assume that the trolleybus was moving uniformly accelerated, so its acceleration is expressed by the formula: a = (V ^ 2 – V0 ^ 2) / 2 * S, where V, V0 are the final and initial speed of the trolleybus, S is the trolleybus path during acceleration.

Since the trolleybus starts its movement from a state of rest V0 = 0 m / s, then a = V ^ 2/2 * S.

a = (15 m / s) ^ 2/2 * 500 m = 0.225 m / s2.

We express the time of movement t from the definition of the body’s acceleration: а = (V – V0) / t.

t = (V – V0) / a.

t = (15 m / s – 0 m / s) / 0.225 m / s2 = 66.6 s.

Answer: the trolleybus moved with an acceleration of a = 0.225 m / s2 for a time of t = 66.6 s.