Derive the equation $v^{2}-u^{2}=2 a S$ graphically.
$(a)$ 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 ?
Prove that if a body is thrown vertically upward, the time of ascent is equal to the time of descent.
What is the nature of motion of a particle depicted by following displacement$-$time graphs ?
A driver of a train travelling at $40\, m s ^{-1}$ applies the breaks as a train enters a station. The train slows down at a rate of $2\, m s ^{-2} .$ The platform is $400\, m$ long. Will the train stop in time ?