Question

Suppose the position s of a particle at time t is given by s(t) = t tant for0 ≤ t ≤ π/3. (a) Find the velocity when t = π/4. (b) Is the particle accelerating or decelerating when t = π/4

Answer 1

to answer part b, you need to see if the second derivative is positive or negative. if the second derivative is positive, that means velocity is increasing (accelerating). if the second derivative is negative, that means velocity is decreasing(decelerating).

Answer 2

Thanks for your answers

Answer 3

\[
s(t) =t \tan (t)\\
s'(t)=\tan (t)+t \sec ^2(t) \\
s''(t)=2 \sec ^2(t)+2 t \tan (t) \sec
^2(t)\\
s''\left(\frac \pi 4\right)=4+ \pi>0\\
\]
The particle is accelerating.