Question

Derive the position velocity equation of motion by graphical method.

(b) Can a body have zero distance covered and non-zero displacement? Explain. ​

Answer 1

Answer:

(a) Shown bellow

(b) No

Explanation:

(a) (2as=v2−u2) by graphical method

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 =21× (sum of parallel sides + distance between parallel sides)

Distance(S)=21(DO+BE)×OE

S=21(u+v)×t...............(i)

we know that,

a=tv−u 

from above equation we can say,

t=av−u...........(ii)

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

S=2a1(u+v)(v−u)

2aS=(u+v)(v−u)

2aS=v2−u2

Hence Proved.

(b) No, it is not possible that a body has zero distance but non zero displacement. Distance cannot be zero because distance is the total path covered but displacement is the shortest route taken to cover the distance. So distance is always greater than displacement.

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