The position of an object moving along x-axis is given by `x=a+bt^(2)` where a = 8.5 m, b = 2.5 `ms^(-2)` and t is measured in seconds. What is its velocity at t = 0s and t = 2-.0s. What is the average velocity between t = 2.0s and t = 4.0s ?

Explanation

In notation of differential calculus, the velocity is
`upsilon=(dx)/(dt)=d/(dt)(a+bt^(2))=2b" "t=5.0" t "ms^(-1)`
At `t=0s, upsilon=0ms^(-1)" and at "t=2.0s, upsilon=10ms^(-1)`
Average velocity `=(x(4.0)-x(2.0))/(4.0-2.0)`
`" "=(a+16b-a-4b)/(2.0)=6.0 times b`
`" "=6.0 times 2.5 =15ms^(-1)`