What speed does a rocket acquire when it moves from rest with an acceleration of 60m / s² on a 3km path?

a = 60 m / s ^ 2.

V0 = 0 m / s.

S = 3 km = 3000 m.

V -?

We express the speed of movement V from the definition for acceleration: a = (V – V0) / t.

V = V0 + a * t.

Since V0 = 0 m / s, then V = a * t.

With uniformly accelerated movement of the body, its movement S is determined by the formula: S = V0 * t + a * t ^ 2/2, where V0 is the initial speed of movement, t is the time of movement, a is the acceleration of the body. since the initial speed is 0 V0 = 0 m / s, the formula will take the form: S = a * t ^ 2/2.

t = √ (2 * S / a).

The formula for determining the rocket speed will take the form: V = a * √ (2 * S / a).

V = 60 m / s ^ 2 * √ (2 * 3000 m / 60 m / s ^ 2) = 600 m / s.

Answer: the rocket will reach a speed of V = 600 m / s.