A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is
A point moves in a straight line so that its displacement $x\,m$ at time $t\,sec$ is given by $x^2 = 1 + t^2$. Its acceleration in $m/sec^2$ at a time $t\,sec$ is
Draw $x \to t$ graph for zero acceleration.