On a spacecraft, two engines are turned on for 910 s at a moment when the velocity of the craft has x and y components of v0x = 5710 m/s and v0y = 7490 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 5.78 x 106 m and y = 6.17 x 106 m. Find the (a) x and (b) y components of the craft's acceleration.

Answer 1

Vox = 5710 m/s
Voy = 7490 m/s

a. Hor. acceleration:
Vo*t + 0.5a*t^2 = 5.78*10^6 m.
5710*910 + 0.5a*910^2 = 5.78*10^6
5.196*10^6 + 4.14*10^5a = 5.78*10^6
4.14*10^5a = 5.84*10^5
a = 1.41 m/s^2.

b. Ver. acceleration:
7490*910 + 0.5a*910^2 = 6.17*10^6
6.816*10^6 + 4.14*10^5a = 6.17*10^6
4.14*10^5a = -6.46*10^5
a = -1.56 m/s^2.