Answer:
The velocity for the particle is (1i+2tj).
Explanation:
Given that,
The particle position is
[tex]r(t)=(t+3)i+(t^2+2)j[/tex]...(I)
In form of x and y
[tex]x(t)=t+3[/tex]....(II)
[tex]y(t)=t^2+2[/tex]...(III)
From equation (II)
[tex]t=x-3[/tex]
Put the value of t in equation (III)
[tex]y=(x-3)^2+2[/tex]
[tex]y=x^2+9-6x+2[/tex]
[tex]x^2-6x-y+11=0[/tex]
We need to calculate the velocity
Velocity is the rate of change of the position of the particle
[tex]v(t)=\dfrac{dr}{dt}[/tex]
[tex]\vec{v(t)}=1i+2t j[/tex]
Hence, The velocity for the particle is (1i+2tj).
