Equations of Motion by Graphical Method

A motorcyclist riding motorcycle $A$ is travelling at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ applies the brakes and stops the motorcycle in $10 \mathrm{s}$. Another motorcyclist of motorcycle $B$ who is travelling at a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ applies the brakes and stops the motorcycle in $20 \mathrm{s}$. Plot speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it comes to a stop?

A car starts from rest and accelerates uniformly at $2 \mathrm{m} {\mathrm{s}}^{-2}$ for $10 \mathrm{s}$. What is its velocity at the end of $10 \mathrm{s}$?

A train starting from rest attains a velocity of $72 \mathrm{km} {\mathrm{h}}^{-1}$ in $5$ minutes. Assuming that the acceleration of the train is uniform, find ($\mathrm{i}$) acceleration of the train ($\mathrm{ii}$) the distance travelled by the train for attaining this velocity.

A car is moving with a uniform velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. The driver of the car decided to overtake a bus moving ahead of car. So the driver of the car accelerates at $1 \mathrm{m} {\mathrm{s}}^{-2}$ for $10 \mathrm{s}$. Find the velocity of the car at the end of $10 \mathrm{s}$. Also, find the distance travelled by the car while accelerating.

A stone is dropped down a deep well from rest. The well is $50 \mathrm{m}$ deep. How long will it take to reach the bottom of well? Given $a=9.8 \mathrm{m} {\mathrm{s}}^{-2}$.

A train starts from rest and accelerates uniformly at $10 \mathrm{m} {\mathrm{s}}^{-2}$ for $1 \mathrm{minute}$. Find the ($\mathrm{i}$) velocity and ($\mathrm{ii}$) distance travelled by the train at the end of $1 \mathrm{minute}$.

A train moving with velocity of $54 \mathrm{km} {\mathrm{h}}^{-1}$ is accelerated so that its velocity becomes $72 \mathrm{km} {\mathrm{h}}^{-1}$ in $15$ seconds. Find the acceleration of the train.

A car is retarded by applying brakes at a rate of $2 \mathrm{m} {\mathrm{s}}^{-2}$. It is finally stopped in $10 \mathrm{s}$. Find its initial velocity.

A bus moving with a velocity of $60 \mathrm{km} {\mathrm{h}}^{-1}$ is brought to rest in $20$ seconds by applying brakes. Find its acceleration.

A bus starts from rest and attains $40 \mathrm{km} {\mathrm{h}}^{-1}$ velocity after $10$ seconds. Calculate the acceleration of the bus in (i) $\mathrm{km} {\mathrm{h}}^{-2}$ (ii) $\mathrm{m} {\mathrm{s}}^{-2}$.