PH 201 Dr. Cecilia Vogel Lecture 4

REVIEW  Acceleration and graphs  derivatives  Constant acceleration  x vs t, v vs t, v vs x OUTLINE  More Constant acceleration  x vs t, v vs t, v vs x  1-D Projectiles, free fall  acceleration of gravity

Special Case: Constant Acceleration  If object’s acceleration has a constant value, a,  then its velocity changes at a constant rate:  And its position changes quadratically with time:

Example A little red wagon is rolling in the positive direction with an initial speed of 10.0 m/s. A child grabs the handle and pulls, giving it a constant acceleration of 5 m/s 2 opposite its initial motion. Let the time the child begins to pull be t=0, and take the position of the wagon at that time to be x=0. a)Where will the wagon be after 1.0 s of pulling? b)How far does it go before coming to a stop (for an instant)?

What if…?  Let’s find a generalization of that:  Where will object be when it’s velocity is v, given a known initial position, velocity, and constant acceleration ? simplify:

Special Case: Free Fall  Object moving with no acceleration except that of gravity. g=9.8 m/s 2

1-D Projectile Motion

Special Case: Dropped Object  Initial velocity is zero  How long will it take an object dropped from height h to hit the ground?  How fast will it be going when it hits?

Special Case: Dropped Object  How long will it take an object dropped from height h to hit the ground? Given v iy = 0 y i = h y= 0 find t

Special Case: Dropped Object  How fast will it be going when it hits? Given y i = h y=0 v iy =0 find v

Opposite of Dropped  Same equation applies to opbject thown up with speed vy, comes to a stop at height h