$A$ man walks on a straight road from his home to a market $2.5 \; km$ away with a speed of $5 \; km \; h^{-1}$. Finding the market closed,he instantly turns and walks back home with a speed of $7.5 \; km \; h^{-1}$. What is the average speed of the man over the interval of time $0$ to $40 \; min$?

$A$ particle is constrained to move on a straight line path. It returns to the starting point after $10\, s$. The total distance covered by the particle during this time is $30\, m$. Which of the following statements about the motion of the particle is false?

$A$ train starting from rest first accelerates uniformly up to a speed of $80 \ km/h$ for time $t$,then it moves with a constant speed for time $3t$. The average speed of the train for this duration of journey will be (in $km/h$):

Which of the following four statements is false?

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

$A$ body is at rest at $x=0$. At $t=0$,it starts moving in the positive $x-$direction with a constant acceleration. At the same instant,another body passes through $x=0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $x_{1}(t)$ after time $t$ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1}-x_{2})$ as a function of time $t$?