There are six kinematic terms. These definitions (really all definitions) should be memorized.

(i) time, t ... this is the reading of a stopwatch

(ii) time interval, D t º t_f - t_i ....difference in two times

(iii) position, r ... vector from an origin to the location of a particle

(iv) displacement, D r º r_f - r_i ...difference in two positions

(v) velocity, v º D r/D t ... this is average velocity over D t,

in the limit D t® 0, this becomes v º dr/dt

v points parallel to the tangent to the path of motion

(vi) acceleration, a º D v/D t ... this is average acceleration over D t,

in the limit D t® 0, this becomes v º dr/dt

· speed is the magnitude of the velocity, \ speed ³ 0

· projectile motion

Place the origin of coordinates not far from the level ground with x-axis horizontal and y-axis vertical (up). In PM there is zero horizontal acceleration and constant (-g) vertical acceleration. The key is each direction behaves independently. These equations are analogous to the free fall equations in one dimension.

x- direction................ y-direction

a_x = 0 ............................. a_y = -g

v_x(t) = v_x(0) ..................... v_y(t) = v_y(0)- gt

x(t) = x(0) + v_x(0)t .......... y(t) = y(0) + v_y(0)t - 0.5 gt²

The above equations can be used to obtain the path of the projectile, i.e. the trajectory, y(x).

· uniform circular motion

We will prove in class that for motion in a circle of radius, r, with constant speed, v, the acceleration vector is

a = (v² / r) [-r(hat)] , this latter vector points to the

center of the circle ® a is centripetal (center seeking) acceleration.

· relative velocity

We show v_PS = v_PS+ v_SS

EXAMPLES [in class]