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Quick Check

Quick Check . A particle moves along a path, and its speed increases with time. In which of the following cases are its acceleration and velocity vectors parallel? When the path is circular When the path is straight When the path is a parabola Never

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Quick Check

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  1. Quick Check • A particle moves along a path, and its speed increases with time. In which of the following cases are its acceleration and velocity vectors parallel? • When the path is circular • When the path is straight • When the path is a parabola • Never • From the same choices above, in which cases are its acclereation and velocity vectors perpendicular everywhere along the path?

  2. Relative Velocity and Acceleration Chapter 4 Section 6

  3. Relative Velocity/FOR • Observer A measures point P at +5 m from the origin • Observer B measures point P at +10 m from the origin

  4. RV/FOR • The man is walking on the moving beltway. • The woman on the beltway sees the man walking at his normal walking speed. • The stationary woman sees the man walking at a much higher speed. • The combination of the speed of the beltway and the walking. • The difference is due to the relative velocity of their frames of reference.

  5. Generalized Relative Velocity • Reference frame SA is stationary • Reference frame SB is moving to the right relative to SA at • This also means that SA moves at – relative to SB • Define time t = 0 as that time when the origins coincide

  6. The positions as seen from the two reference frames are related through the velocity The derivative of the position equation will give the velocity equation is the velocity of the particle P measured by observer A is the velocity of the particle P measured by observer B These are called the Galilean transformation equations. Relative Velocity, equations

  7. Acceleration in Different Frames of Reference • The derivative of the velocity equation will give the acceleration equation. • The acceleration of the particle measured by an observer in one frame of reference is the same as that measured by any other observer moving at a constant velocity relative to the first frame.

  8. Example • A boat crossing a wide river moves with a speed of 10.0 km/hour relative to the water. The water has a uniform speed of 5.00 km/hour due east relative to the Earth. If the boat heads due north, determine the velocity of the boat relative to an observer standing on either bank.

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