Question

(24) Derive an equation for position - velocity relation by graphical method (Draw graph]
2as = y2 - u2
​

Answer 1

Explanation:

Equation for Distance Velocity Relation: Third equation of Motion:

The distance covered by the object moving with uniform acceleration is given by the area of trapezium ABDO

Therefore, Area of trapezium ABDOE

=12×(sum of parallel sides+distance between parallel sides)=12×(sum of parallel sides+distance between parallel sides)

⇒ Distance (s) =12(DO+BE)×OE=12(DO+BE)×OE

⇒s=12(u+v)×t⇒s=12(u+v)×t ----(iii)

Now from equation (ii) a=v−uta=v-ut

∴t=v−ut∴t=v-ut ----(iv)

After substituting the value of tt from equation (iv) in equation (iii)

⇒s=12(u+v)×(v−u)a⇒s=12(u+v)×(v-u)a

⇒s=12a(v+u)(v−u)⇒s=12a(v+u)(v-u)

⇒2as=(v+u)(v−u)⇒2as=(v+u)(v-u)

⇒2as=v2−u2⇒2as=v2-u2

⇒2as+u2=v2⇒2as+u2=v2

⇒v2=u2+2as⇒v2=u2+2as

The above expression gives the relation between position and velocity and is called the third 

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