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 and `t = 2.0 s.` What is the average velocity between `t = 2.0 s and t = 4.0s ` ?

Explanation

(a) `x =a + bt ^(2)`
Differentiating w.r.t time,
`(dx)/(dt) =0 + 2bt`
`therefore v =2bt`
Velocity at `t =0 s, v _((0)) = 0 ms ^(-1)`
Velocity at `t = 2.0 s, v _((2)) = 2 xx 2.5 xx 2`
`= 10 ms ^(-1)`
(b) Position at `t = 4 s, x (4) = a + b (4) ^(2)`
`= 8.5 +2.5 xx 16`
` 8.5+ 40`
` 48.5 m`
Position at `t =2s , x (2) = + b (2) ^(2)`
`=8.5 + 2.5 xx 4`
`=8.5 +10`
`=18.5 m`
`therefore` Average velocity `bar v = (x (4) -x (2))/(4 -2)`
`= (48.5-18.5)/(2) = (30)/(2) `
`therefore bar v = 15 ms ^(-1)`