Question

What value of t is the velocity greatest?

Answer 1

v=12t-6t^2

Find derivative of v

`\\ \sf\longmapsto (dv)/(dx)`

`\\ \sf\longmapsto (d)/(dx)12t-6t^2`

`\boxed{\sf (d(x^n))/(dx)=nx^(n-1)}`

`\\ \sf\longmapsto 12-12t`

Let it be 0

`\\ \sf\longmapsto 12-12t=0`

`\\ \sf\longmapsto 12=12t`

`\\ \sf\longmapsto t=(12)/(12)`

`\\ \sf\longmapsto t=1s`

Answer 2

t = 1

Explanation:

the greatest velocity could be reached:

v' = 0

12 - 12t =0

or 12t =12

t = 12/12

t = 1