Question

how do i solve this?
find the distance traveled in 15 seconds by an object moving with a velocity of v(t) = 20 +7cos(t) feet per second

Answer 1

Velocity is the derivative (rate of change) of position, so position is the integral of velocity. Integrate the function over the range 0 to 15s.

Answer 2

can u show me how? is it just v(t)=20+7cos15?

Answer 3

That will only give you the velocity at time t. You need to integrate that expression to find position. Do you know how to do an integral?

Answer 4

no i dont

Answer 5

Do you understand this:
\[\int\limits\limits_{0}^{15}v(t)dt = \int\limits\limits_{0}^{15}(20+7\cos(t))dt=\int\limits_{0}^{15}20dt + 7\int\limits_{0}^{15}\cos(t)dt\]

Answer 6

no i have never seen that before what does dt stand for? distance x time?

Answer 7

dt means you need to do the integral over the variable t.

I'm surprised they're asking you to do a problem with integrals if you don't know how to do integrals. Integral calculus is a much too difficult subject to teach in an openstudy post.