Question

A spacecraft starts from rest, and makes a journey to a destination 248000 km from its starting point. It does so by accelerating at a constant rate of 15.27 m/s^2 up to the midpoint of the journey, and then decelerates at the same constant rate of 15.27 m/s^2 for the second half of the journey, ending at rest. How long did the entire journey take?

Answer 1

Using 2nd kinematic equation from starting to midpoint:

d1 = U1*t1 + (1/2)*a*t1^2

d1 = distance travelled = 248000/2 km = 1.24*10^8 m

U1 = Initial speed of spacecraft = 0 m/s

a = acceleration = 15.27 m/s^2

So,

2.48*10^8 = 0*t1 + (1/2)*15.27*t1^2

t1 = sqrt (2*1.24*10^8/15.27)

t1 = 4030.01 sec = 4030 sec

Now since rocket starts to de-accelerate at the same rate for same distance, So same time will be taken by it to stop.

Which means t2 = 4030 sec

Total time = 4030 + 4030 = 8060 sec

Since 1 hr = 3600 sec, So

total time = 8060/3600 = 2.24 hrs = 2 hrs 14 min

Let me know if you've any query.