Question

The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time. Question 1 options: 6t3 – 5 5t3 + 6 6t2 + 5 5t2 – 6

Answer 1

6t2+5

Explanation:

Answer 2

(C)
`6t^2+5`

Explanation:

Given the distance, d(t) of a particle moving in a straight line at any time t is:

`d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.`

To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).

`v(t)=(d)/(dt)\\\\v(t) =(d)/(dt)(2t^3 + 5t - 2) =3(2)t^(3-1)+5t^(1-1)\\\\v(t)=6t^2+5`

The correct option is C.