Question

Derive the expression for motion in a plane with constant acceleration​

Answer 1

Answer:

X and Y directions are hence independent of each other.

...

Motion of an object in a plane with constant acceleration

Velocity Velocity in terms of components Displacement

v = v0+ at vx = v0x + axt vy = v0y + ayt r = r0+ v0t+ ½ at2

Answer 2

Motion in two dimension with constant acceleration we we know is the motion in which velocity changes at a constant rate i.e, acceleration remains constant throughout the motion

We should set up the kinematic equation of motion for particle moving with constant acceleration in two dimensions.

Equation's for position and velocity vector can be found generalizing the equation for position and velocity derived earlier while studying motion in one dimension

Thus velocity is given by equation

v=v0+at                                          

where

v is velocity vector

v0 is Initial velocity vector

a is Instantaneous acceleration vector

Similarly position is given by the equation

r-r0=v0t+(1/2)at²                                          

where r0 is Initial position vector

i,e

r0=x0i+y0j

and average velocity is given by the equation

vav=(1/2)(v+v0)                                          (10)

Since we have assumed particle to be moving in x-y plane,the x and y components of equation (8) and (9) are

vx=vx0+axt                                          

x-x0=v0xt+(1/2)axt²                                

and

vy=vy0+ayt                          

y-y0=v0yt+(1/2)ayt²

from above equation 11 and 12 ,we can see that for particle moving in (x-y) plane although plane of motion can be treated as two separate and simultaneous 1-D motion with constant acceleration

Similar result also hold true for motion in a three dimension plane (x-y-z)

Hope it helps it is a nice question