Question

derive an equation describing the relation between displacement and velocity.​

Answer 1

Answer:

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Answer 2

Therefore the equation describing the relationship between displacement and velocity is 'v² - u² = 2as'.

Given:

Let the displacement traveled by an object be 's'.

Let the Velocity of an object be 'v'.

To Find:

Derivation of an equation describing the relationship between displacement and velocity.

Solution:

The given question can be answered as shown below.

Given that,

Let the displacement traveled by an object be 's'.

Let the Velocity of an object be 'v'.

From the figure shown,

Distance traveled by the object in time 't' = Area of the trapezium OABE.

⇒ s = Area of the trapezium OABE

⇒ s = ( 1/2 ) × distance between the parallel sides × sum of lengths of parallel sides.

⇒ s = ( 1/2 ) × ( OE ) × ( OA + BE )  

⇒ s = ( 1/2 ) × t × ( u + v )______(i.)      [ ∵ OA = u; BE = v and OE = t ]

But acceleration of the object is given by, a = ( v - u ) / t

So t = ( v - u ) / a_______(ii.)

From equations (i.) and (ii.),

⇒ s = ( 1/2 ) × ( v - u ) / a × ( u + v )

⇒ s = ( 1/2 ) × ( v² - u² ) / a           [ ∵ ( a + b ) ( a - b ) = a² - b² ]

⇒ ( v² - u² ) = 2as

Therefore the equation describing the relationship between displacement and velocity is 'v² - u² = 2as'.

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