A car travel starting form rest with constant acceleration alpha and reaches a maximum velocity V. It travels with maximum velocity for some time and retards uniformly at the rate of beta and comes to rest. If s is the total distance and t is the total time of journey then t=

A car travel starting form rest with constant acceleration alpha and r

1.	A car travel starting form rest with constant acceleration alpha and reaches a maximum velocity V. It travels with maximum velocity for some time and retards uniformly at the rate of beta and comes to rest. If s is the total distance and t is the total time of journey then t=
Answer» Solution : `V=0+ALPHA t, , t_(1)=v/alpha` `S_(1)=1/2 alpha t_(1)^(2)=v^(2)/(2alpha)` `O-V=beta t_(3), t_(3)=v/beta` `O^(2)-V^(2)=-2]` `S_(3)=v_(2)/(2beta)=1/2 betat_(3)^(2)` `t_(2)=(S_(2))/V=(S-(S_(1)+S_(3)))/(V)=(S-V^(2)/2 (1/alpha+1/beta))/(V)` `t=t_(1)+t_(2)+t_(3)` `=v/alpha+s/v-v/(2alpha)-v/(2beta)+v/(beta), t=s/v+v/2 ((alpha+beta)/(alpha beta))` `s_(2)=s-(s_(1)+s_(2))=s-((v^(2))/(2alpha)+v^(2)/(2alpha))` `=s-v^(2)/(alpha)=s-(vt-s), s_(2)=2s-vt` `[S_(2)`= distance TRAVELLED with constant VELOCITY]