Question

the coordinate of x-y plane are given as x=2+2t+4t^2 and y=4t+8t^2 the motion of this partcile is

Answer 1

Answer:

The co-ordinate of the particle in x-y plane,

x=4t2+2t+2, and  y=8t2+4t

Velocity, Vx=dtdx=8t+2

               Vy=16t+4

Acceleration, ax=dtdVx=8m/s2

                     ay=dtdVy=16m/s2

The acceleration is independent of time, this particle is uniformly accelerated 

x=4t2+2t+2

x−2=4t2+2t. . . .(1)

y=8t2+4t

y=2(4t2+2t). . . .(2)

From equation (1) and (2), we get

y=2(x−2)

y=2x−4

So, the particle is moving along a straight line with slope 2.

The correct option is A.