A motorist starting a car from rest accelerates uniformly to a speed of $v\, m/s$ in $9\, seconds$. He maintains this speed for another $50\, seconds$ and then applies the brakes and decelerates uniformly to rest. His deceleration is numberically equal to three times his previous acceleration. Then the time during which the deceleration takes place is ..........$s$ :-

A body $A$ starts from rest with an acceleration $a_1$ . After $2\ seconds$ , another body $B$ starts from rest with an acceleration $a_2$ . If they travel equal distance in the $5th\ second$ , after the start of $A$ , then the ratio $a_1$ : $a_2$ is equal to

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

A body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are

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

If the velocity-time graph has the shape $AMB$, what would be the shape of the corresponding acceleration-time graph ?