Physics 170 - Mechanics Lecture 9 Relative Motion Vector Motion with Constant Acceleration

Velocity as a function of time:

Position as a function of time: Question

Which of the blue position vs. time graphs goes with this green velocity vs. time graph? The particle’s position at ti = 0 s is xi = −10 m. Relative Motion The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds:

vgnd = 16.2 m/s vgnd = 13.8 m/s Relative Motion This also works in two dimensions:

Observer on ground: sees the sum of two motions one horizontal and one vertical Example: Galilean Relativity

 Observer in the moving frame system: sees only a vertical motion

Observer on ground: sees the sum of two motions one horizontal and one vertical N.B. Without air resistance! Relative Motion

Definition: An Inertial Reference Frame is any coordinate system (or frame of reference) that is either at rest or moving in some direction with a constant velocity. Example: a train or airplane moving forward with a constant speed. Relative Motion

Amy, Bill, and Carlos all measure the velocity of the runner and the acceleration of the jet plane. The green velocity vectors are shown in Amy’s reference frame. What is the runner’s velocity? It depends on the frame of the observer.

Amy: vR = 5 m/s What about a ? Bill: vR = 0 m/s plane

Carlos: vR =−10 m/s Relative Position The position depends on the frame. A set of position observations in one frame can be transformed to get equivalent observations in another frame. Relative Velocity

The velocity also depends on the frame. A set of velocity observations in one frame can be transformed to get equivalent observations in another frame.

z

z’ vpA

A y vAB B y’ x

x’ Example: Crossing a River

You are riding in a boat with a speed relative to the water of vbw = 6.1 m/s. The boat points at an angle of θ = 25° upstream on a river flowing at vwg = 1.4 m/s.

(a) What is your speed vbg and angle θbg relative to the ground? Galilean Relativity

An “inertial frame” is defined to be any reference frame that is at rest or moving with a constant velocity. Consider how the acceleration transforms from frame S to frame S’, an inertial frame that is moving with constant velocity V relative to S. Velocities add, so

Galilean Relativity: While position and velocity are frame- dependent, acceleration is observed to be the same in all inertial reference frames.