Find the distance traveled in 15 seconds by an object moving with a velocity of v(t)=20+7cos(t) feet per second.

Question

ash2326 · Answer

@ccjeff
$$Distance= Velocity \times time $$

ash2326 · Answer

Could you try now?

anonymous · Answer

so it'd be 15*v(t)?
I'm more asking for solving v(t)

ash2326 · Answer

put the value of v(t) given in the question
v(t)=20+7cos(t)

anonymous · Answer

would cos be in radians or degrees?
because i get to 300+105cos(15) and thats all I need to solve for.

ash2326 · Answer

oops, I'm sorry. Do you know integration?

anonymous · Answer

It's been awhile.

anonymous · Answer

integrate the equation wrt to time....make t=0 to find the constant....and then substitute t=15 to find the distance

anonymous · Answer

Okay thank you!

ash2326 · Answer

Sorry I was "out of my mind"
Suppose the body travels a distance ds, during a small time interval dt. During this time, we can consider velocity as constant so
$$ds=vdt$$
distance s is the integral from t=0 to t=15
so we get
$$s=\int_{t=0} ^{t=15} (20+7\cos t) dt$$ feets

anonymous · Answer

u r welcome..