Equations of Motion by Graphical Method

An object starting from rest travels $20 \mathrm{m}$ in first $2 \mathrm{s}$ and $160 \mathrm{m}$ in next $4 \mathrm{s}$. What will be the velocity after $7 \mathrm{s}$ from the start?

An electron moving with a velocity of $5\times {10}^4 \mathrm{m} {\mathrm{s}}^{-1}$ enters into a uniform electric field and acquires a uniform acceleration of ${10}^4 \mathrm{m} {\mathrm{s}}^{-2}$ in the direction of its initial motion. How much distance the electron would cover in this time?

An electron moving with a velocity of $5\times {10}^4 \mathrm{m} {\mathrm{s}}^{-1}$ enters into a uniform electric field and acquires a uniform acceleration of ${10}^4 \mathrm{m} {\mathrm{s}}^{-2}$ in the direction of its initial motion. Calculate the time in which the electron would acquire a velocity double of its initial velocity.

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_1$ and $u_2$ respectively. Prove that the heights reached by them would be in the ratio of ${u_1}^2:{u_2}^2$ (Assume upward acceleration is $-g$ and downward acceleration to be $+g$).

Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between $4th$ and $5th$ seconds.

An object is dropped from rest at a height of $150$metre and simultaneously another object is dropped from rest at a height $100$metre. What is the difference in their heights after $2 \mathrm{s}$ if both the objects drop with same accelerations? How does the difference in heights vary with time? 

A car starts from rest and moves along the x-axis with constant acceleration $5 \mathrm{m} {\mathrm{s}}^{-2}$ for $8$ seconds. If it then continues with constant velocity, what distance will the car cover in $12$ seconds since it started from the rest?

How will the equation of motion for an object moving with a uniform velocity change?