A particle moves in a straight line so that at time t its displacement from a fixed origin is x and its velocity is v. If its acceleration is 4 + x and v = 1 when x = 0, what is v when x = 1?
The value of
Recall that the derivative of velocity is acceleration and the anti-derivative of acceleration is velocity.
#int 4 +x dx = 1/2x^2 + 4x + C#
We can now solve for
#1/2(0)^2 + 4(0) + C =1#
#C = 1#
Therefore the velocity function is
Hopefully this helps!