Position Formula and Example

Position Formula :

The position formula the rate of change the displacement when a change in position takes place is Δx is equal to the presuming the golf ball moves from position x2.minus x1 in meter. Hence position formula can be written as

Δx =x2(m) –x(m)

The position formula rate change in position at any moment of time X(t)(s)  in second is equal to the one to two the product of the acceleration the body possesses α (rad/s2) in radsecter2 multiply the square of body with time is t2(s) in second and addition of velocity of the body v0(m/s) in meter per second and multiply the body with time t(s) in second and addition of initial position of the body a x0.Hence the position formula can be written as

X(t)(s) = 1/2 *α (rad/s2) * t2(s) +v0(m/s) *t(s) +x0

Where,
the position of the body with time t → x(t)

the initial velocity of the body→ v0

the acceleration the body possesses → α in rad/s

the initial position of the body →x0

Sample Problems :

Example 1 :

Calculate the position of the person at the end time 4s if the initial velocity of the person is 8m/s and angular acceleration is 3 m/s2?In a  person travels 60m distance.

Solution :

Known,

V0 =8 m/s

X0 =60m

α =3 m/s

t= 4s

The change in position of the  person at time t is

X(t) = 1/2 α t2 +v0 t +x0

X(4)=1/2 ×3 ×(4)2+8 ×4+60

X(4)=24+32+60

X(4)=116m

Example 2 :

Calculate the position of the person at the end time 3s if the initial velocity of the person is 4m/s and angular acceleration is 5 m/s2? In a person travels 90m distance. .

Solution :

Known,

V0 =4 m/s

X0 =90m

α =5m/s

t= 3s

The change in position of the  person at time t is

X(t) = 1/2 α t2 +v0 t +x0

X(3)=1/2 ×5 ×(3)2+4 ×3+90

X(3)=22.5+102

X(3)=124.5 m

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