Physics Problem, Help Please!?

Question

On a spacecraft, two engines are turned on for 889 s at a moment when the velocity of the craft has x and y components of v0x = 5710 m/s and v0y = 6240 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 5.68 x 106 m and y = 6.91 x 106 m. Find the (a) x and (b) y components of the craft's acceleration.

Answer 1

you can use the relation between displacement and acceleration ;
Delta X= 1/2 ax t^2 + V0x t
Delta Y= 1/2 ay t^2 + V0y t

substituting V0x=5710m/s , V0y=6240 m/s , t= 889s
Delta X= 5.68 x 10^6 m , Delta Y =6.91 x 10^6 m
we get :
5.68 x 10^6 = 1/2 ax (889)^2 + 5710 * 889
0.4 x 10^6 ax = 5.68 x 10^6 - 5.07 x 10^6
canceling 10^6 from both sides we get;
0.4 ax = (5.68 - 5.07)
ax = 1.52 m/s^2
ay can be calculated in the same way.
ay= 3.42 m/s^2

Answer 2

Displacement due to acceleration from Vo is:
(x) = 5.68E6 - 5710*889 = 6.04E+05
(y) = 6.91E6 - 6240*889 = 1.36E+06

Acceleration = 2xt^-2:
(x) = 2 * 6.04E+05/889^2 = 1.53 ms^-2
(y) = 2 * 1.36E+06/889^2 = 1.72 ms^-2