Question

position of a particle in gravity free space is varying with time is given as x = 2t and y= 1/2 t2 ,where x and y are in m and t is in s .the equation of path of the particle is

a . y = 4x2
b. y= X2 / 4
c. y= X2/8
d. y=8x2​

Answer 1

Given:

Position of a particle in gravity free space is varying with time is given as x = 2t and y= 1/2 t2 ,where x and y are in m and t is in sec.

To find:

Equation of trajectory of particle ?

Calculation:

Since , this is an example of two dimensional motion of an object, the equation of trajectory has to be expressed in forms of "y" and "x".

$1) \: \: \: \: \: \: x = 2t \\ \implies t = \dfrac{x}{2} \: \: \: \: \: ......(i)$

$2) \: \: \: y = \dfrac{1}{2} {t}^{2}$

Putting value of "t" from eq.(i) :

$\implies \: y = \dfrac{1}{2} \times {( \dfrac{x}{2}) }^{2}$

$\implies \: y = \dfrac{1}{2} \times \dfrac{ {x}^{2} }{4}$

$\implies \: y = \dfrac{ {x}^{2} }{8}$

• So, from the equation , we can very well understand that the object will follow a parabolic trajectory with concavity towards y axis.

So, the required equation of trajectory is:

$\boxed{ \bold{\: y = \dfrac{ {x}^{2} }{8} \: \: \: \: \: \: \: .......(parabolic \: equation)}}$