Question #089b1
1 Answer
Dec 22, 2016
Kinematic equation of interest is
v(t)=u+at .....(1)
wherev(t) is velocity after timet ,u is initial velocity of an object anda is constant acceleration experienced by it.
- Recall the expression
Displacement=Velocity×time - Observe it looks like equation of a straight line in the form
y=mx+c .
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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
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+12at2