$A$ motorbike starts from rest, attains a velocity of $10 \,m/s$ with an acceleration of $0.5 \,m/s^2$, travels $10 \,km$ with this uniform velocity, and then comes to a halt with a uniform deceleration of $0.2 \,m/s^2$. The total time of travel is: (in $\,s$)

$A$ person of height $1.6 \ m$ is walking away from a lamp post of height $4 \ m$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60 \ cm \ s^{-1}$,the speed of the tip of the person's shadow on the ground with respect to the person is . . . $cm \ s^{-1}$.

$A$ body of mass $m$ moving along a straight line covers half the distance with a speed of $2 \,ms^{-1}$. The remaining half of the distance is covered in two equal time intervals with a speed of $3 \,ms^{-1}$ and $5 \,ms^{-1}$ respectively. The average speed of the particle for the entire journey is

$A$ body is projected vertically up with a velocity $v$ and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

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 $..........\,m/s$.

$A$ particle moving along a straight line covers the first half of the distance with a speed of $3 \, m \, s^{-1}$. The other half of the distance is covered in two equal time intervals with speeds of $4.5 \, m \, s^{-1}$ and $7.5 \, m \, s^{-1}$ respectively. The average speed of the particle during the motion is: