Find initial velocity of the spaceship

[TyFelmingham]

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

 

[PhysicsMajor]

Yes you will have to integrate.

 

[TyFelmingham]

Yes you will have to integrate.

How do you integrate that?

 

[xanthym]

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

a(t) = (dv/dt) = 3 - 2t ::: ⇒ v(t) = ∫ (3 - 2t) dt = 3t - t² + v₀
v(t) = (dz/dt) = 3t - t² + v₀ ::: ⇒ z(t) = ∫ (3t - t² + v₀) dt = 3t²/2 - t³/3 + v₀t + z₀

Problem requires that {z(5) = z₀}, so that:
z(5) = z₀ = 3(5)²/2 - (5)³/3 + v₀(5) + z₀
⇒ 0 = (37.5) - (41.7) + 5v₀
⇒ 5v₀ = 4.2
⇒ v₀ = (0.84 m/sec)


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