Sketch Vector Functions: r(t), r'(t) for t=1

[Physicsnoob90]

Homework Statement

(a) Sketch the plane with the given vector expression
(b) find r'(t)
(c) sketch the position vector r(t) and the tangent vector r'(t) for the given value of t

r(t) = <t^2,t^3> t=1

Homework Equations

The Attempt at a Solution

1) i derived the equation : r'(t) = <2t,3t^2>
2) sub in t=1: r(t)=<1,1>
r'(t)=<2,3>

I've always been a terrible graphing person so if anyone can help me improve on this, it would be really helpful

 

[Simon Bridge]

Please show your working and reasoning.

 

[HallsofIvy]

Do you understand that, in the xy-plane, r= <t^2, t^3> covers the same curve as x= t^2, y= t^3? Have you just calculated a number of (x, y) points for different t to help in drawing the curve? For example when t= 0, x and y are both 0 so (0, 0) is a point on the curve. When t= 1 the point is (1, 1). When t= -1, (1, -1), when t= 2, (4, 8), when t= 1/2, (1/4, 1/8), etc.