Question

write the three equations of motion and derive V=u +at.​

Answer 1

Explanation:

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Answer 2

Question :-

(i) Write the Three Equations of Motion

(ii) Derive the Equation :- v = u + at

Solutions :-

(i) The Three Equations of Motion are as follows -

- Equation for VELOCITY - TIME Relation : v = u + at

- Equation for POSITION - TIME Relation : $\bold {s = ut + \frac{1}{2} at^2}$

- Equation for POSITION - VELOCITY Relation : $\bold {2as = v^2 - u^2}$

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(ii) Consider the Velocity - Time Graph of an Object that moves under Uniform Acceleration as Given in the Attachment.

From the Graph,

The Initial Velocity of the Object is u and it increases to v in Time t. The Velocity changes at a Uniform Rate a

From the Graph, it's clear that

BC = BD + DC

BC = BD + OA

So, we have -

v = BD + u   ...Eq. 1

From the Velocity - Time Graph, the Acceleration of the Object is given by -

a = Change in Velocity / Time Taken = BD / AD

a = BD / OC = BD / t   ...Eq. 2

Putting Eq. 2 in Eq. 1, we get -

v = u + at which is the Equation of Velocity - Time Relation