Question

A car starts from rest at time t = 0 and accelerates at -0.6t+

4 meters/sec^2 for
. how long does it take for the car to go 100meters?

Answer 1

Explanation:

Given

car start from rest at t=0

`a=-0.6t+4 m/s^2`

`\frac{\mathrm{d} v}{\mathrm{d} t}=a`

`\frac{\mathrm{d} v}{\mathrm{d} t}=-0.6t+4`

`dv=(-0.6t+4)dt`

integrating

`\int dv=\int \left ( -0.6t+4\right )dt`

`v=-0.3t^2+4t+c`

at
`t=0\ v=0`

thus
`c=0`

`v=-0.3t^2+4t`

`\frac{\mathrm{d} s}{\mathrm{d} t}=v`

`ds=vdt`

integrating

`\int ds=\int vdt`

`\int ds=\int (-0.3t^2+4t)dt`

`s=-0.1t^3+2t^2+c`

at
`t=0\, s=0`

thus
`c=0`

`s=-0.1t^3+2t^2`

at
`s=100`

`0.1t^3-2t^2+100=0`

Solving cubic equation

`t=10\ s\ ,t=16.18\ s, t=-6.18\ s`

Neglecting negative value of t

we get
`t=10 s`