this question is designed to be answered without a calculator. an objects velocity at time t is given by the…

this question is designed to be answered without a calculator. an objects 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 = 3π/4 is -2. -1. 3. 4.

this question is designed to be answered without a calculator. an objects 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 = 3π/4 is -2. -1. 3. 4.

Answer

Explanation:

Step1: Recall displacement formula

Displacement $s=\int_{a}^{b}v(t)dt$, here $a = 0$, $b=\frac{3\pi}{4}$ and $v(t)=2\cos(2t)$.

Step2: Integrate the velocity function

$\int 2\cos(2t)dt=\sin(2t)+C$.

Step3: Evaluate the definite - integral

$\int_{0}^{\frac{3\pi}{4}}2\cos(2t)dt=\left[\sin(2t)\right]_{0}^{\frac{3\pi}{4}}$. Substitute the upper and lower limits: $\sin(2\times\frac{3\pi}{4})-\sin(2\times0)$. $\sin(\frac{3\pi}{2})-\sin(0)=- 1 - 0=-1$.

Answer:

-1