Question #089b1

1 Answer
Dec 22, 2016

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.

  1. Recall the expression
    Displacement=Velocity×time
  2. Observe it looks like equation of a straight line in the form
    y=mx+c.

![revisionworld.com](useruploads.socratic.org)

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)dt .....(2)

If we integrate both sides we get
ds(t)=tt0(u+at)dt
s(t)=tt0(u+at)dt ......(3)
We see that LHS of the equation is total displacement, and RHS is area under the velocity-time graph from time t0 to t.
Equation (3) is the required expression.

One should not be surprised if one calculates integral of RHS of equation (3) from time t=0 to t, one actually obtains the other kinematic equation

s=ut+12at2