Answer:
a=
- [tex]40 ms^{-2} for 0\leq t\leq 1[/tex]
- [tex]20ms^{-2} for 1\leq t\leq 4[/tex]
- [tex]-20ms^{-2} for 4\leq t\leq \infty[/tex]
Step-by-step explanation:
We will find the acceleration in 3 intervals of time(t) and those intervals are:
- [tex]0\leq t\leq 1[/tex]
- [tex]1\leq t\leq 4[/tex]
- [tex]4\leq t\leq\infty[/tex]
We know that acceleration(a) is given by [tex]a= \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t}[/tex]=Slope of velocity-time graph
In interval [tex]0\leq t\leq 1[/tex],
[tex]a=Slope= \frac{\Delta v}{\Delta t}=\frac{40-0}{1-0} =40ms^{-2}[/tex]
In interval [tex]1\leq t\leq 4[/tex],
[tex]a=Slope= \frac{\Delta v}{\Delta t}=\frac{100-40}{4-1} =20ms^{-2}[/tex]
In interval [tex]4\leq t\leq\infty[/tex],
[tex]a=Slope= \frac{\Delta v}{\Delta t}=\frac{60-100}{6-4} =-20ms^{-2}[/tex]
