Notes for 11.3 11.4 - Calculus III - 11.3 Velocity and...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Calculus III - 11.3 – Velocity and Acceleration Definition of Velocity and Acceleration If x and y are twice-differentiable functions of t , and r is a vector-valued function given by r ( t) = x(t) I + y(t) j , then the velocity vector, acceleration vector and speed at time t are as follows: Velocity = v ( t) = r (t) = x’(t) i + y’(t) j Acceleration = a (t) = r ’’ (t) = x’’(t) i + y’’(t) j Speed = [ ] [ ] 2 2 ) ( ) ( ) ( ' ) ( t y t x t r t v + = = For motion along a space curve, the definitions are extended in the normal way. Examples: #6 (What do you notice about the velocity and acceleration vectors at the point?) #12
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Position Function for a Projectile Neglecting air resistance, the path of a projectile launched from an initial height h with initial speed v 0 and angle of elevation θ is described by the vector function ( 29 ( 29 j gt t v h i t v t r - + + = 2 0 0 2 1 sin cos ) ( θ where g is the gravitational constant. #36
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

Page1 / 4

Notes for 11.3 11.4 - Calculus III - 11.3 Velocity and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online