The velocity of a delivery robot on a straight aisle is modelled by v={8−2t,0≤t≤3,5−t,3<t≤7.v=\begin{cases}8-2t,&0\leq t\leq3,\\ 5-t,&3<t\leq7.\end{cases}v={8−2t,5−t,0≤t≤3,3<t≤7.
Show that the velocity is continuous at t=3t=3t=3.
Find all times in 0≤t≤7 0\leq t\leq7\,0≤t≤7 when the particle is instantaneously at rest.
Find the total distance travelled in the first 7 s.