velocity time graph of a particle moving in a straight line at show in the figure at=0 x=+10 in which region particle is moving towards the origin
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= Addition of modulus of different area i.e., s=∫|v|dt
Total displacement A1+A2+A3
= Addition of different area considering their sign.
i.e., r=∫vdt
Area above time axis is taken as positive, while area below time axis is taken as negative.
Here A1 and A2 are area of triangle 1 and 2 respectively and A3 is the area of trapezium.
Calculation of Acceleration : Let AB is a velocity-time graph for any moving particle
As Acceleration =Change in velocityTime taken
=v2−v1t2−t1 …(i)
From triangle ABC, tanθ=BCAC=ADAC
=v2−v1t2−t1 …(ii)
By comparing (i) and (ii)
Acceleration (a) = tanθ
It is clear that slope of tangent on velocity-time graph represents the acceleration of the particle.
Various velocity -time graphs and their interpretation
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