$A$ man moves in an open field such that after moving $10 \, m$ on a straight line,he makes a sharp turn of $60^{\circ}$ to his left. The total displacement just at the start of the $8^{\text{th}}$ turn is equal to ........ $m$.

$A$ 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

$A$ particle moving in a straight line covers half the distance with speed $6 \, m/s$. The other half is covered in two equal time intervals with speeds $9 \, m/s$ and $15 \, m/s$ respectively. The average speed of the particle during the motion is: (in $ \, m/s$)

Select the incorrect statement among the following$:-$
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.

$A$ 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 $\,m/s$)

Which of the following four statements is false?