Question

Suppose that a particle's position is described by r(t)=(t+3)i+(t2+2)j. Give an equation (in the form of a formula involving x and y set equal to 0 ) whose solutions consist of the path of the particle. Find the velocity vector for the particle: v(t)

Answer 1

Answer:

The velocity for the particle is (1i+2tj).

Explanation:

Given that,

The particle position is

$r(t)=(t+3)i+(t^2+2)j$...(I)

In form of x and y

$x(t)=t+3$....(II)

$y(t)=t^2+2$...(III)

From equation (II)

$t=x-3$

Put the value of t in equation (III)

$y=(x-3)^2+2$

$y=x^2+9-6x+2$

$x^2-6x-y+11=0$

We need to calculate the velocity

Velocity is the rate of change of the position of the particle

$v(t)=\dfrac{dr}{dt}$

$\vec{v(t)}=1i+2t j$

Hence, The velocity for the particle is (1i+2tj).