Question

A space craft flying in a straight course with a velocity of 75 km /s fire rocket motors for 6 s . At the end of this time its speed is 120 km / s in the same direction. Find a) The spacecraft average acceleration when the motors were firing b) the distance travelled by the space craft in first 10 s after the rocket motors were started ,the motors have being in action for 6 s.

Answer 1

Use kinematic equations:
SUVAT
s-displacement, u-initial velocity, v-final velocity,a- acceleration, t-time
v=u + at
v2 = u2 + 2as
s=1/2(u+v)t
s=ut + 1/2at2

a)Calculate the average acceleration when the motors were firing:
av. acceleration = change in velocity   =    120 - 75    =  45m/s   = 7.5m/s2
                                          time                              6s              6s

therefore the average acceleration = 7.5km/s^2

b)Distance traveled after the rockets were fired:
- Find distance traveled during the 6s when the motors were firing:
t=6s, v=120 km/s, u=75km/s, a=7.5km/s2
 
s= 1/2(u+v)t
  = 1/2(120+75)6
  =1/2 x 195 x 6
  = 585 km
-Find distance after the motors are fired:(the next 4 seconds to make it 10 seconds)
After the motors are fired, the craft moves with 120km/s speed
That means in 4s = 4 x 120
                          = 480km
add the distance traveled in the 10s =  (585 + 480)km
                                                    = 1065km
Therefore the total distance traveled = 1065 km

Answer 2

here's ur answer... I am sure that thos answer is correct