A bus accelerated from rest at a constant rate `alpha` for some time, after which it decelerates at a constant rate `beta` to come to rest. If the total time elapsed is t seconds. Then evaluate following parameters from the given graph
(a) the maximum velocity achieved.
(b) the total distance travelled graphically and
(c) Average velocity.

Explanation

(a). `alpha="slope of line" OA=(v_(max))/(t_(1))impliest_(1)=(v_(max))/(alpha)`
`beta="slope of line" AB=(v_(max))/(t_(2))impliest_(2)=(v_(max))/(beta)`
`t=t_(1)+t_(2)=(v_(max))/(alpha)+(v_(max))/(beta)=v_(max)((alpha+beta)/(alphabeta))`
`v_(avg)=((alphabeta)/(alpha+beta))`
(b). Displacement`=` area under the v-t graph
`=(1)/(2)xx "base" xx "height" =(1)/(2)(t_(1)+t_(2))v_(max)=(1)/(2)tv_(max)`
`=(1)/(2)((alphabeta)/(alpha+beta))t^(2)`
`v_("avg")=("total displacement")/("total time")=(1)/(2)((alpha beta)/(alpha+beta))t=(v_(max))/(2)`