A train starting from rest travels the first part of its journey with constant acceleration $a$ , second part with constant velocity $v$ and third part with constant retardation $a$ , being brought to rest. The average speed for the whole journey is $\frac{{7v}}{8}$. The train travels with constant velocity for $...$ of the total time

- A
$0.75$

- B
$0.87$

- C
$0.83$

- D
$1.28$

For the velocity-time graph shown in the figure, in a time interval from $t=0$ to $t=6\,s$, match the following columns.

Colum $I$ | Colum $II$ |

$(A)$ Change in velocity | $(p)$ $-5 / 3\,Sl$ unit |

$(B)$ Average acceleration | $(q)$ $-20\,SI$ unit |

$(C)$ Total displacement | $(r)$ $-10\,SI$ unit |

$(D)$ Acceleration at $t=3\,s$ | $(s)$ $-5\,SI$ unit |

Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity $(v_0)$ and the braking capacity, or deceleration, $-a$ that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of $v_0 $ and $a$.

The acceleration-time graph of a body is shown below The most probable velocity-time graph of the body is

Position time graph of a particle moving along straight line is shown which is in the form of semicircle starting from $t=2$ to $t=8 \,s$. Select correct statement

A scooter accelerates from rest for time $t_{1}$ at constant rate $a _{1}$ and then retards at constant rate $a _{2}$ for time $t _{2}$ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be ..... .

- [JEE MAIN 2021]