Question

The position function for a particular object is s equals negative 31 over 2 times t squared minus 44 times t plus 85. Which of the following statements is true?

Answer 1

Answer : The correct option is, The initial velocity is -44

Step-by-step explanation :

As we are given the position function expression:

`S=-(31)/(2)t^2-44t+85`

As we know that, differentiation of position function with respect to 't' gives velocity function.

`(dS)/(dt)=(d(-(31)/(2)t^2-44t+85))/(dt)`

`v=-2* (31)/(2)t-44`

`v=-31t-44`

At time t = 0, the initial velocity will be:

`v=-31(0)-44`

v = -44

Hence, the correct option is, The initial velocity is -44

Answer 2

Answer: The initial velocity is - 44

Explanation:

S =
`(-31)/(2)`
`t^(2)` - 44t + 85 .

Differentiating once to get the velocity , we have

V = - 31t - 44

The initial velocity means that t = 0 , substitute this into the equation , we have

V = -31 (0) - 44

V = -44

Therefore, the initial velocity is -44