Practice Question 2

Question

An object’s velocity at time t is given by the function v(t) = 2 cos(2t). The displacement of the object from time t = 0 to t = 3pi/4 is

–2.

–1.

3.

4.

Answer 1

S = ∫₀^3π/4(2cos(2t)dt = sin(2t)₀^3π/4 = sin(3π/2) - sin(0) = - 1

Answer is -1

Answer 2

To find the displacement of an object, we integrate its velocity function with respect to time. This will be a definite integral, where the limits of integration are the start and end times (in this case, t = 0 and t = 3π/4). What do you get when you take that integral?