The v-s graph describing the motion of a motorcycle is shown in figure. Construct the a-s graph of the motion and determine the time needed for the motorcycle to reach the position `s=120 m.` Given In `5 = 1.6.`

Answer

A

Explanation

For `0 lt sle60 m`
`v=12/60s+3=3+s/5`
`(dv)/(dt)=(1/5).(ds)/(dt)`
`=1/5(v) =1/5(3+s/5)=3/5+s/25…..(i)`
or `a=3/5+s/25`
i.e. a-s graph is a straight line.
At `s=0, a=3/5m//s^2=0.6m//s^2`
and at `s=60m, a=3.0m//s^2`
For `s gt 60m`
v=constant
`:. a=0`
Therefore, the corresponding a-s graph is shown in
figure.

From Eq. (i), `(dv)/(dt)=v/5`
or `int_3^v (dv)/v=1/5 int_0^t dt`
`ln (v/3) =t/5`
`:. v=3e^(t//5)` or `int_0^60 ds=3int_0^(t_1) e^(t//5)dt`
`60=15(e^(t_1)//5)-1)` or `t_1=8.0s`
Time taken to travel next 60m with speed `15 m//s`
will be `60/15=4s`
`:.` Total time `=12.0s`