The problem involves determining the initial velocity of a spaceship given its acceleration function, a(t) = 3 m/s² – (2 m/s³)t, with the condition that it returns to its starting point after 5 seconds.
The discussion includes various attempts at integration and deriving equations of motion. Some participants provide guidance on the integration process, while others express uncertainty about the steps involved.
There is a focus on ensuring that the position of the spaceship after 5 seconds is equal to its initial position, which introduces specific conditions for the problem. The original poster and others express confusion about the integration process and the implications of the problem's requirements.
How do you integrate that?PhysicsMajor said:Yes you will have to integrate.
a(t) = (dv/dt) = 3 - 2t ::: ⇒ v(t) = ∫ (3 - 2t) dt = 3t - t2 + v0TyFelmingham said:a) The acceleration of a spaceship is given by a(t) = 3 m/s2 – (2 m/s3 ) t. Find the initial velocity V0 so that the spaceship is at the same point where it started after 5 seconds.
No idea how to do this one, but do you need to integrate?
Ty