Question

Please help me find this part of my question, thank you!

Answer 1

Given,

`s(t)=(1)/(3)t^3-(7)/(2)t^2+10t`

To find: Find all the times when his velocity is increasing.

Solution:

Differentiate the given equation with respect to time for v(t)

`\begin{gathered} (ds(t))/(dt)=(3)/(3)t^2-(7)/(2)*2t+10 \\ v(t)=t^2-7t+10 \end{gathered}`

Now, v(t)=0

`\begin{gathered} t^2-7t+10=0 \\ t^2-5t-2t+10=0 \\ t(t-5)-2(t-5)=0 \\ (t-2)(t-5)=0 \end{gathered}`

The time is

`t=2,5`

Thus, all the times when his velocity is increasing is 2, 5.