KINEMATICS

I. CONCEPTS

A.DISPLACEMENT: (D r) = r - r0


B. VELOCITY: vavg = (D r)/(D t) becomes v = dr/dt


C. ACCELERATION: aavg = (D v)/(D t) becomes a = dv/dt


II. EQUATIONS OF MOTION FOR a=constant vector

v = v0 + at

r - r0 = v0t + (1/2)at2

vavg = (v0 + v)/2

v2 = v02 + 2a(r-r0)



NOTE THAT a IS CONSTANT IN MAGNITUDE AND DIRECTION

III. FOR 1-DIMENSIONAL MOTION THESE SIMPLIFY

vx = v0x + axt

x - x0 = v0xt + (1/2)ax t2

vavgx = (v0x + vx)/2

vx2 = v0x2 + 2ax(x - x0)

APPLICATIONS

An airplane lands on a runway and must stop.  How long is the runway?

a) How much time is needed to stop?










IV. OBJECTS IN FREE-FALL ACCELERATE DOWNWARD AT 9.8 m/s2 (32 f/s2 )








APPLICATIONS

A ball is thrown upward at a speed of 64 f/s.

a) How high does it rise?








b) How long is it in the air?










c)When is it at a height of 32 f?














d) When does it have a velocity of 64 f/s downward?