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?

1 Answer
May 22, 2018

The value of v is 11/2

Explanation:

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 C.

1/2(0)^2 + 4(0) + C =1

C = 1

Therefore the velocity function is v= 1/2x^2 + 4x+ 1 and the value of v at x = 1 is hence v(1) = 1/2 + 4 + 1 = 11/2

Hopefully this helps!