the position function of an object is d(t)= t^5/2 (t-7), t ≥ 0, where d is in metres and t is in seconds. when is the object stopped? and how do you know when the acceleration is positive?

Answer 1

The function is ambiguously written. I assume you mean t^5/2 (t-7) but it could be (t⁵/2) * (t-7) or some people mean (incorrectly) t⁵/(2(t-7)). I will just give you the steps to solution.

"stopped" is when v = 0. Let's call position r instead of d. set v = dr/dt = 0 and find times when this is true. Use product rule to differentiate.

The acceleration = d²r/dt² = dv/dt can be calculated as a function of t. Find its zeroes and test one point in the region to determine if a is > or < than 0 in that region.

Please consider a tutor. Take care.