Drive the relationship between position &time graphically
Answers
A big part of the science of physics involves measuring the motion of objects, from a ball to a steam train. This includes plotting an object's position, velocity, acceleration and other relevant data. The graphical representation of one form of motion can lead to the graphs of the other forms of motion. For instance, the velocity-time graph is derived from the position-time graph. Similarly, the acceleration-time graph is derived from the velocity-time graph. The slopes of each graph relate to the various graphical representations of motion.
See pic, Let a body moves from D to with initial speed u and are moving with uniform acceleration finally body reach point B after time taken t.
distance travelled by body = area between curve v-t
= area DBA + area DAEO
= 1/2 × base × height + length × Breadth
= 1/2 × t × (v - u) + ut
we know , ( v - u ) = at, put it above
= 1/2× t × at + ut
= ut + at²/2
hence , distance travelled by body = ut + 1/2at²
