Question

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

Given V(t) = –2 sin t and S(0) = 0, we integrate V(t) to find S(t), resulting in S(t) = A. 2 cos t.

Step-by-step explanation:

To find the object's position function s(t) from its velocity function v(t) = –2 sin t, we need to integrate the velocity function. Since s(0) = 0, the constant of integration will be zero. Thus, integrating gives us s(t) = –(–2 cos t), which simplifies to s(t) = 2 cos t. The negative sign is cancelled due to the double negative from the integral of sine turning into cosine. However, without the initial condition, we could have a constant added, but s(0) = 0 dictates that the constant is zero.

Therefore, the correct answer is A. 2 cos t.