The maximum possible acceleration of a train moving on a straight track is $10\ m/s^2$ and maximum possible retardation is $5 \ m/s^2.$ If maximum achievable speed of train is $10\ m/s$ then minimum time in which train can complete a journey of $135\ m$ starting from rest and ending at rest, is.........$s$
$5$
$10$
$15$
$20$
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
The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement
A particle of mass $m$ moves on the x-axis as follows : it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $ t= 1$ at the point $x = 1$. No other information is available about its motion at intermediate time $(0 < t < 1)$. If $\alpha $ denotes the instantaneous acceleration of the particle, then