CHAPTER 3

Displacement, Velocity, and Acceleration

Equations of Kinematics in 2 Dimensions

Projectile Motion

Relative Velocity

Displacement

The displacement vector of an object is drawn from the initial position vector to the final position vector. The magnitude of the initial plus the displacement will be the final position vector:

rf = r0 + r

Therefore, the displacement vector can be found by finding the difference. r = rf – r0

See figure 3.1 pg 59

Velocity and Acceleration

The velocity and acceleration calculations do not change in two dimensions. It is simply important to remember 2 things: The x and y components must be treated

individually and then added together The direction is important since these are

vector quantities. A change in direction will result in an acceleration, even if the magnitude of the velocity is not changing. Ex: Check for understanding 1, pg 60, Pg 82 # 3, 7,9

Equations of Kinematics 2D

If an object moves in the horizontal and vertical direction at the same time, we assign horizontal motion with an x (vx, ax), and vertical motion with a y (vy, ay)

See table 3.1 page 61 !! It is important to realize that the x part

of the motion occurs exactly as it would if the y part did not occur at all. Similarly, the y part of the motion occurs exactly as it would if the x part of the motion did not exist.

Pg 65 #2, pg82-83 #15, 17, 19

Projectile Motion

Projectile motion results when an object is thrown either horizontally through the air or at an angle relative to the ground. This will result in the object moving through the air with a constant horizontal velocity while falling freely under the influence of gravity. The resulting path of the projectile is called a trajectory and has a parabolic shape.

Motion of a projectile is broken down into constant velocity and zero acceleration in the horizontal direction and changing vertical velocity due to acceleration of gravity in the vertical direction.

Kinematic Equations for Projectiles Horizontal Motion Vertical motion

Ax = 0 ay = g = -9.81 m/s2

Vx = x/t vy = voy + g t

X = vx t y = voy t + ½ g t2

*notice the minus sign in the equations for vertical motion. Since the acceleration g and the initial vertical velocity are in opposite directions, we must give one of them a negative sign. Horizontal velocity of projectiles is constant, vertical velocity is changed by gravity

Pg 82 # 21, 27, 29, 33, 43

Relative Velocity

When adding vectors of one object’s motion relative to another, we use the ordering of the subscript symbols in a definite pattern. The first subscript refers to the body that is moving while the second letter indicates the object relative to which the velocity is measured. Ex. Vpt where p is the passenger and t is a train that the

passenger has a specific velocity relative to the train. See example pg 74.

This can help add vectors to determine relative velocity of other objects with problems that have multiple frames of reference. By definition,

Vpt = -Vtp

Pg 81 #14, 15, pg 85 #55, 57, 61