The space rocket accelerates from rest and, having traveled 200 km, reaches a speed of 11 km / s.

The space rocket accelerates from rest and, having traveled 200 km, reaches a speed of 11 km / s. with what acceleration is the rocket moving? what is the acceleration time?

Given:

V0 = 0 m / s – the initial velocity of the rocket is zero;

V1 = 11 km / h = 11 * 10 ^ 3 m / s – rocket speed after acceleration;

S = 200 kilometers = 200 * 10 ^ 3 meters – the distance traveled during acceleration.

It is required to determine the acceleration time t (seconds) and the rocket acceleration a (m / s ^ 2).

S = V0 * t + a * t ^ 2/2 = a * t ^ 2/2 = V1 * t ^ 2 / (2 * t) = V1 * t / 2, hence:

t = 2 * S / V1 = 2 * 200 * 10 ^ 3/11 * 10 ^ 3 = 400/11 = 36.4 seconds.

a = (V1 – V0) / t = V1 / t = 11 * 10 ^ 3 / 36.4 = 11000 / 36.4 = 302.2 m / s ^ 2.

Answer: the acceleration of the rocket is 302.2 m / s ^ 2, the acceleration time is 36.4 seconds.