Question

I would appreciate some help for this worksheet question​

Answer 1

a)
`v(2.5\,s) = 40\,(m)/(s)`, b)
`v(3.5\,s) = -60\,(m)/(s)`, c)
`v(4.5\,m) = 0\,(m)/(s)`, d)
`v(7.5\,s) = 60\,(m)/(s)`

Step-by-step explanation:

Mathematically speaking, the instantaneous velocity is the slope of the curve, which can be estimated by means of the definition of secant line, equivalent to the definition of average velocity:

`v(t) = (x(t+0.5\,s)-x(x-0.5\,s))/((t+0.5\,s)-(t-0.5\,s))` (1)

Where:

`x(t+0.5\,s)`,
`x(t-0.5\,s)` - Position of the particle at
`t +0.5\,s` and
`t-0.5\,s`, measured in meters.

`t` - Time, measured in seconds.

Now we proceed to calculate each instantaneous velocity:

a)
`t = 2.5\,s`

`v(2.5\,s) = (x(3\,s)-x(2\,s))/(3\,s-2\,s)`

`v(2.5\,s) = (120\,m-80\,m)/(1\,s)`

`v(2.5\,s) = 40\,(m)/(s)`

b)
`t = 3.5\,s`

`v(3.5\,s) = (x(4\,s)-x(3\,s))/(4\,s-3\,s)`

`v(3.5\,s) = (60\,m-120\,m)/(1\,s)`

`v(3.5\,s) = -60\,(m)/(s)`

c)
`t = 4.5\,s`

`v(4.5\,s) = (x(5\,s)-x(4\,s))/(5\,s-4\,s)`

`v(4.5\,s) = (60\,m - 60\,m)/(1\,s)`

`v(4.5\,m) = 0\,(m)/(s)`

d)
`t = 7.5\,s`

`v(7.5\,s) = (x(8\,s)-x(7\,s))/(8\,s-7\,s)`

`v(7.5\,s) = (0\,m - (-60\,m))/(1\,s)`

`v(7.5\,s) = 60\,(m)/(s)`