The document discusses kinematic equations and examples of their use. It introduces four common kinematic equations used to relate variables like displacement (x), velocity (v), acceleration (a), and time (t). It then provides examples of using the equations to solve for unknown variables, like using the kinematic equation relating displacement and time to find how far a ball rolls down a ramp before slowing. It also discusses free fall as a special case and provides an example of using the kinematic equations to find the time for an object to fall halfway from the top of a building.

1. BY NIYA WATKINS, SARAH GIMONT, AND JACKIE PFEIFFER Kinematic Equations

2. kinematic Equations 1) V=a t +V o 2) X=½ a t 2 +V o t + X o 3) V 2 = v o 2 +2a(X-X o ) 4) X =½(V+V o ) t +X o

3. kinematics We have 6 variables when dealing with kinematic equations X, X o , V, V o , a, and t however, when attempting to solve the equations, one variable will be omitted and one variable will be the unknown

4. Kinematics Example problem: Niya pushes a ball down a ramp with a speed of 3 m/s. As the ball rolls, it loses speed at a rate of 5 m/s. How far does the ball roll before it comes back up? .9 m

5. kinematics Sample Problem: explanation First, we must figure out which variables we have we know Vo=3(the starting speed), that Vo=0(the starting point), X=?(how far...), and a=-5(the rate the speed decreases at) We now know we can use equation 3 0=9 + -10(x)

6. free fall A special case of constant acceleration. Secrets: Acceleration is -9.8 m/s 2 Stop at the top Symmetry (time up = time down)

7. free fall Example Problem: Sarah drops a ball off a building that it 200m tall. How long does it take it to fall halfway? 4.52s

8. free fall Example Problem: Explanation First, we must figure out which variables we have We know X o =0(the origin), X=200(the height of the building), V o =0(the ball is dropped), a=-9.8(rule of free fall), and t=?(how long…) So we would use equation 2 200=-4.9t 2* * remember we need to have a real answer