$A$ car starts from rest and moves with a constant acceleration of $5 \,m/s^2$ for $10 \,s$ before the driver applies the brake. It then decelerates for $5 \,s$ before coming to rest. The average speed of the car over the entire journey is: (in $\,m/s$)

$A$ 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

$A$ bogie of a uniformly moving train is suddenly detached from the train and stops after covering some distance. What is the relation between the distance covered by the bogie and the distance covered by the train in the same time?

Mark the correct statements for a particle moving in a straight line.

An aircraft is flying at a height of $3400 \; m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0 \; s$ apart is $30^{\circ}$,what is the speed in $m/s$ of the aircraft?

The equation of motion of a body is $\frac{dv}{dt} = -4v + 8$,where $v$ is the velocity in $m/s$ and $t$ is the time in seconds. The initial velocity of the particle was zero. Then,