Question

IS ANYONE HERE GOOD AT CALCULUS?? IF SO, PLEASEEEE HELP ME!!!! An object’s velocity at time t is given by v(t) = –2 sin t. Let s(t) represent the object’s position at time t. If s(0) = 0, then s(t) = A) 2 cos t. B) –2 cos t. C) 2 cos t – 2. D) –2 cos t + 2.

Answer 1

Answer: C

Step-by-step explanation:

Since we are given velocity, which is the first derivative, we have to fidn the antiderivative of velocity to get position.

∫-2sint dt

s(t)=2cos(t)+C

Since we are given s(0)=0, we can plug in the values to find C, constant.

0=2cos(0)+C

0=2(1)+C

0=2+C

C=-2

Now that we know our constant, we can find out position.

s(t)=2cos(t)-2