A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for sometimes to come to rest. If the total time taken is t . The maximum velocity of car is given by :

Step-by-step solution

Let car acceleates for time t₁ and decelerates for time t₂ then t₁+t₂=t .....(1) From v=u+a t aligned & v =u+a t₁ v & =a t₁ aligned For deceleration aligned & v=u-a t & 0=a t₁-b t₂ ( u=v) & a t₁=b t₂ & t₂= a t₁ b & t₁+ a t₁ b =1 [From Eq. (1)] & t₁ (1+ a b )=t & t₁= b t a+b & aligned Maximum velocity of car v=a t₁= a b t a+b