Question

derive equation for position velocity relation v²-u²=2asplz ​

Answer 1

Explanation:

Let the initial velocity of the object = u

Let the object is moving with uniform acceleration, a.

Let object reaches at point B after time, t and its final velocity becomes, v

Draw a line parallel to x-axis DA from point, D from where object starts moving.

Draw another line BA from point B parallel to y-axis which meets at E at y-axis.

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

Therefore,

Area of trapezium ABDOE =

1/2× (sum of parallel sides + distance between parallel sides)

Distance(S)= 1/2(DO+BE)×OE

S= 1/2(u+v)×t...............(i)

we know that,

a= v-u/t

from above equation we can say,

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

After substituting the value of t from equation(ii) in equation (i)

S= 1/2a(u+v)(v−u)

2aS=(u+v)(v−u)

2aS=v ^2-u^2

Hence Proved.

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Answer 2

a = dv/dt *ds/ds ( numerator and denominator

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