Question

a rocket ship has 3 stages. the first stage takes the rocket from rest to 50m/s in 30s, the second stage takes the rocket from 50m/s to 120m/s in 25s and the final stage takes it from 120m/s to 150m/s in 12s. m/s²
what is the acceleration of the rocket during stage 1?
what is the acceleration of the rocket during stage 2?
what is the acceleration of the rocket during stage 3?

Explanation:

Step1: Recall acceleration formula

The formula for acceleration is $a=\frac{v - u}{t}$, where $v$ is final - velocity, $u$ is initial - velocity and $t$ is time.

Step2: Calculate acceleration for stage 1

For stage 1, $u = 0$ m/s, $v = 50$ m/s and $t = 30$ s. Substitute into the formula: $a_1=\frac{50 - 0}{30}=\frac{5}{3}\approx1.67$ m/s².

Step3: Calculate acceleration for stage 2

For stage 2, $u = 50$ m/s, $v = 120$ m/s and $t = 25$ s. Substitute into the formula: $a_2=\frac{120 - 50}{25}=\frac{70}{25}=2.8$ m/s².

Step4: Calculate acceleration for stage 3

For stage 3, $u = 120$ m/s, $v = 150$ m/s and $t = 12$ s. Substitute into the formula: $a_3=\frac{150 - 120}{12}=\frac{30}{12}=2.5$ m/s².

Answer:

Acceleration in stage 1: $\frac{5}{3}$ m/s²
Acceleration in stage 2: 2.8 m/s²
Acceleration in stage 3: 2.5 m/s²