Question

A rocket in deep space starts from rest at t=0 s with acceleration of 2.50 m/s^2. How far it has gone in 10.0s

Answer 1

The rocket would have gone 125 m away in deep space.The speed when it has gone 300 m is 76.7 m/s.

Answer:

The distance the rocket traveled is 125 m. The speed when it has gone 300 m is 76.7 m/s.

Explanation:

According to the equations of motion, if an object is moving with constant acceleration, then the distance travelled by the object with that acceleration and within a specific time can be obtained as

$s=ut+\frac{1}{2}at^{2}$

Since the initial velocity is given as u = 0 at t = 0. Then at t = 10 s, the acceleration is given by 2.5 m/$s^{2}$.

Thus,

s= 0 + ($\frac{1}{2}$×2.5×$10^{2}$)=125 m.

Thus, the rocket would have gone 125 m away in deep space.

Similarly, if it had gone 300 m then its speed can be determined using the third equation of motion.

$2as = v^{2} -u^{2}$

Since, here v is unknown and u is known as 0 with a = 2.5 m/$s^{2}$.

2× 9.8×300=v²

5880=v²

Thus, the speed v = $\sqrt{5880}=76.7 m/s$

So, the speed when it has gone 300 m is 76.7 m/s.