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 target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of iron plate is $2\,cm$. A bullet fired goes through the wood first and then penetrates $1\,cm$ into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates $2\,cm$ into wood. If $a_1$ and $a_2$ be the retardations offered to the bullet by wood and iron plates respectively, then

Equation of motion of a body is $\frac{d v}{d t}=-4 v+8$, where $v$ is the velocity in $m / s$ and $t$ is the time in second. Initial velocity of the particle was zero. Then,

A train accelerates from rest at a constant rate $\alpha$ for distance $x_1$ and time $t_1$. After that it retards to rest at constant rate $\beta$ for distance $x_2$ and time $t_2$. Which of the following relations is correct?

A body starts from rest with an acceleration $a_{1},$ after two seconds another body $B$ starts from rest with an acceleration $a _{2}$. If they travel equal distance in fifth second, after the starts of $A$, the ratio $a _{1}: a _{2}$ will be equal to

The acceleration-time graph for a body is shown in the graph. Which of the following  graphs would probably represent velocity of the body plotted against time:-