Question

Derive an equation for velocity-time relation graphically ​

Answer 1

Let FE = time, t Now, from the graph, BE = AB + AE

⇒ v = DC + OD

Since, AB = DC and AE = OD ⇒

v = DC + u

OD = u ⇒

v = DC + u

Now, Acceleration

(a) =(Change in velocity)/(Time taken) a= v – ut

⇒ a = v - ut ⇒

a = OC – OD t = DC t ⇒

a = OC-OD t =DC t ⇒

at=DC ⇒at=DC

v= at + u v = at + u ⇒ v = u + at ⇒ v = u + at

Above equation is the relation among initial velocity (u), final velocity (v), acceleration (a) and time (t). It is called first equation of motion.