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Obtain the equations of motion by graphical method: (a) Equation for velocity-time relation. (b) Equation for displacement-time relation. (c) Equation for displacement-velocity relation.

Vidyadip · Accepted Answer

(a) Velocity-time graph: shows the change in velocity with time of a uniformly accelerated object. The object starts from the point D in the graph with velocity v. Its velocity keeps increasing and after time t it reaches the point B on the graph.The initial velocity of the object = u = OD

https://pg-data.sgp1.digitaloceanspaces.com/chapter_wise/15897/Q5.png" alt="Image" width="230" height="" />
(b) Suppose that an object is in uniform acceleration ‘a’ and it has covered the distance ‘s’ within time’t’. From the graph the distance covered by the object during time’t’ is given by the area of quadrangle DOEB.https://pg-data.sgp1.digitaloceanspaces.com/chapter_wise/15897/Q6.png" alt="Image" width="325" height="" />
(c) We can determine the distance covered by the object in time t from the area of the quadrangle DOEB. DOEB is a trapezium. So we can use the formula for its area.https://pg-data.sgp1.digitaloceanspaces.com/chapter_wise/15897/Q7.png" alt="Image" width="335" height="" />This is Newton’s third equation of motion.

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