# Question #089b1

##### 1 Answer

Kinematic equation of interest is

#v(t)=u+at# .....(1)

where#v(t)# is velocity after time#t# ,#u# is initial velocity of an object and#a# is constant acceleration experienced by it.

- Recall the expression

#"Displacement"="Velocity"xx"time"# - Observe it looks like equation of a straight line in the form

#y=mx+c# .

We know that velocity is rate of change of displacement, therefore equation (1) can be written as

#(ds(t))/(dt)=u+at#

#=>ds(t)=(u+at)cdot dt# .....(2)

If we integrate both sides we get

We see that LHS of the equation is total displacement, and RHS is area under the velocity-time graph from time

Equation (3) is the required expression.

One should not be surprised if one calculates integral of RHS of equation (3) from time

#s=ut+1/2at^2#