$(a)$ Write differences between speed and velocity.
$(b)$ The speed of a moving object is $x m s ^{-1}$. Its velocity is $y m s ^{-1}$. What is the similarity observed ?
$(a)$ Speed is distance travelled per unit time, whereas velocity is displacement per unit time. Speed cannot be zero, displacement can be zero.
$(b)$ Both have the same units.
A cyclist travels a distance of $4\, km$ from $P$ to $Q$ and then moves a distance of $3\, km$ right angle to $PQ$. Find his resultant displacement graphically.
How can you find the following ?
$(i)$ Velocity from a displacement$-$time graph.
$(ii)$ Acceleration from velocity$-$time graph.
$(iii)$ Displacement from velocity$-$time graph.
$(iv)$ Velocity from acceleration$-$time graph.
The distance$-$time graph of two trains are given below. The trains start simultaneously in the same direction.
$(i)$ How much ahead of $A$ is $B$ when the motion starts ?
$(ii)$ What is the speed of $B$ ?
$(iii)$ When and where $A$ will catch $B$ ?
$(iv)$ What is the difference between the speeds of $A$ and $B$ ?
$(v)$ Is the speed of either trains uniform or non uniform ? Justify your answer.
Distance$-$time graph below represents the motion of two buses $A$ and $B$
$(i)$ What is the distance by which bus $B$ was ahead of bus $A$ initially ?
$(ii)$ Do they ever meet each other ? If so, when ?
$(iii)$ What is the distance travelled by bus $A$ when it overtakes bus $B$ ?
$(iv)$ Find out the distance by which bus $A$ was ahead of bus $B$ at $y=12 h$
$(v)$ Which one of them is moving faster ? Give reason.
A train starting from rest picks up a speed of $10\, m s ^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the nert $50\, s$. Plot a speed$-$time graph for the entire motion of the train.
$(i)$ acceleration of the train while accelerating,
$(ii)$ retardation of the train while retarding,
$(iii)$ and the total distance covered by the train.