Motion in Space: Velocity and Acceleration

[Physicsnoob90]

Homework Statement

For V(t) = (1+t)i + (t^2-2t)j find:

1. velocity
2.Acceleration
3. speed/length
4. Unit Tangent
5. tangential component
6. normal component at t=2

Homework Equations

The Attempt at a Solution

1. v'(t) = <1,2t-2> = <1, 2(t-1)>
2. a(t) = <0,2>
3. length = Square root of (1+4(t-1)^2)
4. Unit Tangent = <1,2(t-1)> / square root (1+4(t-1)^2)
from here I'm stuck trying to find the tangential component and normal component. [/B]

 

[Ray Vickson]

Homework Statement

For V(t) = (1+t)i + (t^2-2t)j find:

1. velocity
2.Acceleration
3. speed/length
4. Unit Tangent
5. tangential component
6. normal component at t=2

Homework Equations

The Attempt at a Solution

1. v'(t) = <1,2t-2> = <1, 2(t-1)>
2. a(t) = <0,2>
3. length = Square root of (1+4(t-1)^2)
4. Unit Tangent = <1,2(t-1)> / square root (1+4(t-1)^2)
from here I'm stuck trying to find the tangential component and normal component. [/B]

First decide: normal and tangential component of WHAT? In general, if you have two vectors $\vec{a}, \vec{b}$ the component $\vec{a}_{||}$ of $\vec{a}$ parallel to $\vec{b}$ and the component $\vec{a}_{\perp}$ perpendicular to $\vec{b}$ are
$$\vec{a}_{||} = \frac{\vec{a} \cdot \vec{b}}{\vec{b} \cdot \vec{b}} \vec{b} \\ \vec{a}_{\perp} = \vec{a} - \frac{\vec{a} \cdot \vec{b}}{\vec{b} \cdot \vec{b}} \vec{b}$$