The velocity of a particle moving along the $x$-axis is given by $V = x^2 - 5x + 4$ (in $\text{m/s}$), where $x$ denotes the $x$-coordinate of the particle in metres. The magnitude of the acceleration of the particle when the velocity is zero is:

The relation between time $t$ and distance $x$ is $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The relation between acceleration $a$ and velocity $v$ is:

$A$ horse rider covers half the distance with $5\,m/s$ speed. The remaining part of the distance was travelled with speed $10\,m/s$ for half the time and with speed $15\,m/s$ for the other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7}\,m/s$. The value of $x$ is

$A$ cyclist traversed half the distance of a linear track with a velocity $10 \ m \ s^{-1}$. The remaining part of the track was covered with a velocity $v_1$ for half the time and a velocity $v_2$ for the other half of the time. If $v_1+v_2=20 \ m \ s^{-1}$, then the average velocity of the cyclist during the completion of the journey through the track is (in $m \ s^{-1}$)

$A$ car moves towards north at a speed of $54 \,km/h$ for $1 \,h$. Then it moves eastward with the same speed for the same duration. The average speed and velocity of the car for the complete journey is ..........

Two particles $P$ and $Q$ simultaneously start moving from point $A$ with velocities $15\,m/s$ and $20\,m/s$ respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When $P$ overtakes $Q$ at $B$,then its velocity is $30\,m/s$. The velocity of $Q$ at point $B$ will be $..........\,m/s$.