Question

2. a. If an object's position is given by F(t) 5)t3, find the speed of the object at t -1 sec. b. Is the object speeding up or slowing down at t 1 sec?

Answer 1

r(t) = 5cos($\pi$t²) + t³

differentiate with respect to t, we get

v(t) = 5* -sin($\pi$t²). 2$\pi$t + 3t²

at t = 1

v(1) = -10 sin ($\pi$). $\pi$ + 3

v(1) = 3 m/s

Now, to find if particle is speeding up or slowing down, we need to find acceleration vector.

which comes out as positive. So, speed is increasing