Derivation of Equations for Uniformly Accelerated Motion Using Calculus

As soon as a car just starts from rest in a certain direction, a scooter moving with a uniform speed overtakes the car. Their time-speed $(t-v)$ graphs are shown in the adjoining figure. Calculate from the graph the acceleration of the car initially.

The figure shows the time-distance $(t-s)$ graphs of two cars which start simultaneously in the same direction. Calculate from the graph After how much time and at which place the car $B$ will catch car $A$?

The figure shows the time-distance $(t-s)$ graphs of two cars which start simultaneously in the same direction. Calculate from the graph which car is moving faster? What their speeds are?

The figure shows the time-distance $(t-s)$ graphs of two cars which start simultaneously in the same direction. Calculate from the graph by how much distance the car $A$ was ahead of car $B$ initially.

Derive the following relation either graphically or mathematically:

$v^2=u^2+2as$