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$(a)$ Draw velocity-time graph for the following cases
$(i)$ When the object is at rest.
$(ii)$ When the object is thrown vertically upwards.
$(b)$ A motorcyclist riding motorcycle $A$ who is travelling at $36\, km h^{-1}$ applies the brakes and stops the motorcycle in $10\, s$. Another motorcyclist of motorcycle $B$ who is travelling at $18\, km h^{-1}$ applies the brakes and stops themotorcycle in $20\, s$. Plot speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it come to a stop ?
Solution
For motorcycle $A$,
$u=36 km h ^{-1}$
$=\frac{36 \times 5}{18}=10 ms ^{-1}$
$v=0$
$t=10 s$
For motorcycle $B,$
$u=18 km h ^{-1}$
$=\frac{18 \times 5}{18}=5 ms ^{-1}$
$v=0$
$t=20 s$
Distance travelled by $A$ before stopping
$=$ Area of triangle $OPQ$
$=\frac{1}{2} \times 10 \times 10=50 m$
Distance travelled by $B$ before stopping
$=$ Area of triangle $OMN =\frac{1}{2} \times 20 \times 5=50 m$
Hence, both motorcycles travel same distance before they come to a stop.
