Question

If u(t) = 6t 1.9 m/s and s = 2 m when t 0, find expressions for a(t) and s(t). Calculate values for s(t), v(t), and a(t) for times t = 0, 1, 2, and 3 seconds and tabulate the results.

Answer 1

t in s 0 1 2 3

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s in m 2 4.068 17.44 55.05

a in m/s² 0 11.4 21.27 30.64

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Step-by-step explanation:

Given:

u(t) =
`6t^(1.9)`

s = 2 m at t = 0

Now,

u(t) =
`\frac{\textup{ds}}{\textup{dt}}`

thus,

`\frac{\textup{ds}}{\textup{dt}}=6t^(1.9)`

or

`ds=6t^(1.9)dt`

on integrating, we get

`\int \, ds=\int{6t^(1.9)} \, dt`

or

s =
`(6\ t^(1.9+1))/(1.9+1)+c`

here c is the integration constant

s =
`(6\ t^(2.9))/(2.9)+c`

now, at t = 0, s = 2 m

thus,

2 =
`(6*0^(2.9))/(2.9)+c`

or

c = 2

hence,

the expression is

s =
`(6*t^(2.9))/(2.9)+2`

also,

a(t) =
`\frac{\textup{du}}{\textup{dt}}`

or

a(t) =
`\frac{\textup{d(6t^(1.9))}}{\textup{dt}}`

or

a(t) =
`6*1.9* t^(1.9-1)`

or

a(t) =
`11.4* t^(0.9)`

now,

at t = 0

s =
`(6*0^(2.9))/(2.9)+2`

or

s = 2 m

and,

a =
`11.4* 0^(0.9)`

or

a = 0 m/s²

at t = 1

s =
`(6*1^(2.9))/(2.9)+2`

or

s = 4.068 m

and,

a =
`11.4* 1^(0.9)`

or

a = 11.4 m/s²

at t = 2

s =
`(6*2^(2.9))/(2.9)+2`

or

s = 17.44 m

and,

a =
`11.4* 2^(0.9)`

or

a = 21.27 m/s²

at t = 3

s =
`(6*3^(2.9))/(2.9)+2`

or

s = 55.05 m

and,

a =
`11.4* 3^(0.9)`

or

a = 30.64 m/s²

t in s 0 1 2 3

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s in m 2 4.068 17.44 55.05

a in m/s² 0 11.4 21.27 30.64

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