Question

If a body moves in a straight line according to the law s = 24t + 3t2 - t3 , where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body's velocity as a function of time. A. V = 30t - t2 B. V = 24 + 6t - 3t2 C. V = 24 + 3t - t2 D. V = 30t - 3t2

Answer 1

Remember that the velocity as a function of time is the derivative of the position as a function of time.
To solve this we are going to take the derivative of our position function
`s=24t+3t^2-t^3`. To do that er are going to apply the power rule of calculus:
`(dy)/(dx) x^n=nx^(n-1)`


`(dy)/(dx) 24t+(dy)/(dx)3t^2-(dy)/(dx)t^3`

`24+2(3)t-3t^2`

`v=24+6t-3t^2`

We can conclude that the correct answer is: B. V = 24 + 6t - 3t2