A motor bike running at $5\, m s ^{-1}$, picks up a velocity of $30\, m s ^{-1}$ in $5\, s$. Calculate $(i)$ acceleration $(ii)$ distance covered during acceleration.
$u=5 m s ^{-1} ; v=30 m s ^{-1} ; t=5 s ; a=? ; S =?$
$(i)$ Applying $v=u+a t$
$30=5+a \times 5$
$5 a=25$ or $a=5 m s ^{-2}$
$(ii)$ Applying $v^{2}-u^{2}=2 a S$
$(30)^{2}-(5)^{2}=2 \times 5 \times S$
Or $875=10 \times S$
Or $S=87.5 m$
The displacement $-$ time graph of a body is parallel to time axis. What will you infer about the velocity of the body ?
In a long distance race, the athletes were expected to take four rounds of the track such that the line of finish was same as the line of start. Suppose the length of the track was $200\, m$.
$(a)$ What is the total distance to be covered by the athletes ?
$(b)$ What is the displacement of the athletes when they touch the finish line ?
$(c)$ Is the motion of the athletes uniform or nonuniform ?
$(d)$ Is the displacement of an athlete and the distance moved by him at the end of the race equal ?
Study the speed$-$time graph of a body given below and answer the following questions
$(i)$ What type of motion is represented by $OA, AB$ and $BC$ ?
$(ii)$ Find positive and negative accelerations of the body.
$(iii)$ Find the distance travelled by the body from $A$ to $B$.
"The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration". Give an example to justify this statement
Out of the three speed$-$time graphs shown below
Identify the graph for the following cases.
$(i)$ A ball thrown vertically upwards and returning to the hand of the thrower ?
$(ii)$ A body decelerating to a constant speed and accelerating.