SOLUTION: The acceleration of an object after t seconds is a(t)=t^2+5ms^-2 . If the velocity at t=2 was 6ms^-1 , what was the velocity at t=4?

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Question 258677: The acceleration of an object after t seconds is a(t)=t^2+5ms^-2 . If the velocity at t=2 was 6ms^-1 , what was the velocity at t=4?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Acceleration is the derivative of velocity.
You can integrate to find velocity.
a=t%5E2%2B5
v=%281%2F3%29t%5E3%2B5t%2BC
Use the condition to solve for C.
6=%281%2F3%29%288%29%2B5%282%29%2BC
C=6-8%2F3-10=-20%2F3
v%28t%29=%281%2F3%29t%5E3%2B5t-20%2F3
v%284%29=%281%2F3%29%2864%29%2B5%284%29-20%2F3
v%284%29=104%2F3