Describing Motion §3.1–3.2 (and 2-D)

Vectors Position is a vector Velocity is a vector Acceleration is a vector

CPS Question A B C D E F G H vivi vfvf What is the direction of  v?

CPS Question A B C D E F G H vivi vfvf What is the direction of  v?

CPS Question A B C D E F G H vivi vfvf What is the direction of  v?

CPS Question A B C D E F G H vivi vfvf What is the direction of  v?

CPS Question A B C D E F G H vivi vfvf What is the direction of  v?

Describing 3-Vectors Position r = x i + y j + z k Velocity v = dr/dt = dx/dt i + dy/dt j + dz/dt k = v x i + v y j + v z k Acceleration a = dv/dt = d 2 x/dt 2 i + d 2 y/dt 2 j + d 2 z/dt 2 k = a x i + a y j + a z k

Magnitudes of 3-Vectors Distance from origin r = | r | = x 2 + y 2 + z 2 Speed v = | v | = v x 2 + v y 2 + v z 2 Magnitude of acceleration a = | a | = a x 2 + a y 2 + a z 2

Vectors Position and velocity may be in different directions Velocity and acceleration may be in different directions

Familiar Situations Ballistic trajectories Circular motion If a || v, path is straight. If a || v, path is curved.

CPS Question If an object’s distance from the origin r does not change, its velocity must be zero. A.True. B.False.

CPS Question If an object’s speed v does not change, its acceleration must be zero. A.True. B.False.

Acceleration and Velocity The component of a perpendicular to v causes the direction to change. The component of a parallel to v causes the speed to change.

CPS Question The rate of change of an object’s speed d|v|/dt is the same as the magnitude of its acceleration |dv/dt|. A.Always. B.Sometimes. C.Never.