Question

On a spacecraft, two engines are turned on for 738s at a moment when the velocity of the craft has x and y components of v0x = 2555 m/s and v0y = 6275 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 4.24 x 10⁶ m and y = 7.32 x 10⁶ m. Find the x and y components of the craft's acceleration.

Please explain

Answer 1

Using the equation of motion :

s = ut + 0.5*a*t^2

s = displacement = 4.24*10^6 i + 7.32*10^6 j

u = 2555 i + 6275 j

t = 738 s

So, 4.24*10^6 i + 7.32*10^6 j = (2555 i + 6275 j )*738 + 0.5*a*738^2

So, ( 4.24*10^6 i + 7.32*10^6 j ) - (2555 i + 6275 j )*738 = 0.5*a*738^2

So, 2.35*10^6 i + 2.69*10^6 j = 0.5*a*738^2

So, a = 8.63 i + 9.87 j  

So, x-component of acceleration = 8.63 m/s2 <------- answer

and the y-component = 9.87 m/s2 <-------- answer