# Chapter 3: Motion, Acceleration, and Forces

## Section 1: Describing Motion

• Motion

• Every day you see objects and people in motion.

• One way to describe motion is to say that it is fast or slow. However, sometimes you might need to know the speed of an object, as well as the direction in which it is moving.

• You don’t always need to see something move to know that motion has taken place.

• Motion occurs when an object changes position.

• To measure the position of an object, a reference frame must be chosen.

• Reference Frame: a group of objects that are not moving relative to each other

• An object does not have absolute motion, but only motion relative to a chosen reference frame.

• Displacement: the distance and direction of an object’s final position from its initial position.

• Displacement includes both a size and a direction.

• The size of the displacement is the distance between the initial and final position

• Vector: A quantity that is specified by both a size and a direction

• Displacement includes both a size and a direction and is an example of a vector.

• Speed

• Speed: the distance an object travels per unit of time.

• In SI units, the unit of speed is meters per second (m/s).

• Instantaneous Speed: the speed at a single instant of time.

• Average Speed: the total distance traveled divided by the total travel time.

• average speed (in meters/second) = total distance (in meters)/total time (in seconds)

• Velocity

• Velocity: the speed of the object and its direction of motion.

• Just like displacement, velocity is a vector that has a size and a direction. The size of an object’s velocity is the object’s speed.

• Objects have different velocities if they are moving at different speeds, or in different directions.

• The velocity of an object can change even if the speed of the object remains constant.

• Graphing Motion

• The motion of an object over a period of time can be shown on a distance-time graph.

• Time is plotted along the horizontal axis of the graph and the distance traveled is plotted along the vertical axis of the graph.

• If the object moves with constant speed, the increase in distance over equal time intervals is the same

• The slope of a line on a distance-time graph equals the speed

• A horizontal line on a distance-time graph has zero slope, and represents an object at rest.

• On a distance-time graph, the distance is plotted on the vertical axis and the time on the horizontal axis.

• Each axis must have a scale that covers the range of numbers to be plotted.

## Section 2: Acceleration

• Acceleration: the change in velocity divided by the time for the change to occur.

• Just as velocity has a size and direction, acceleration also is a vector that has a size and direction.

• A change in velocity can be either a change in how fast something is moving or a change in the direction of movement. Any time a moving object changes direction, its velocity changes and it is accelerating.

• Calculating Acceleration

• When an object moves from one place to another, it might speed up, slow down, and change direction many times.

• When acceleration is changing, the size of the average acceleration over some period of time can be calculated.

• average acceleration (in m/s^2) = (final velocity in m/s - initial velocity (in m/s)) / (final time (s) - initial time (s))

• For an object moving in one direction, the acceleration can be found from a speed-time graph. For this type of graph, the vertical axis is the object’s speed and the horizontal axis is the time. Then the slope of the plotted line is the size of the object’s acceleration.

• A speed-time graph tells you if acceleration is a positive or negative number.

## Section 3: Motion and Forces

• Force: a push or pull that one object exerts on another.

• Just like velocity and acceleration, force also is a vector that has a size and a direction.

• The size of a force often is called the strength of the force.

• The direction of a force is the direction in which the push or pull is applied.

• A force can cause the motion of an object to change.

• Balanced Forces

• Force does not always change velocity.

• Net Force: When two or more forces act on an object at the same time

• Balanced Forces: Forces on an object that are equal in size and opposite in direction

• Unbalanced Forces: When forces combine to produce a net force that is not zero, the forces acting on the object

• When the forces acting on an object are balanced, the velocity of an object doesn’t change.

• The velocity of any object changes only when the forces on it are unbalanced.

• Friction: the force that opposes the sliding motion of two surfaces that are in contact.

• The size of the frictional force exerted by one surface on another depends on the materials the surfaces are made from and the roughness of the surfaces.

• The frictional force between two surfaces increases when the force pushing the surfaces together increases.

• Friction is due to the micro-welds that form between two surfaces in contact. These micro-welds become stronger when the force pushing the surfaces together increases.

• Static Friction: the frictional force that prevents two surfaces in contact from sliding past each other.

• Sliding Friction: the frictional force that prevents two surfaces in contact from sliding past each other.

• Rolling Friction: When an object rolls over a surface, a frictional force due to rolling friction slows the object down.

• Air resistance: opposes the motion of objects that move through the air.

• Air resistance causes objects to fall with different accelerations and different speeds.

• Air resistance acts in the direction opposite to the velocity of an object moving in air.

• The size of the air resistance force depends on the size and shape of an object.

• The amount of air resistance on an object depends on the speed, size, and shape of the object.

• As an object falls, the downward force of gravity causes the object to accelerate.

• However, as the speed of a falling object increases, the upward force of air resistance also increases.

• The terminal velocity is the highest velocity the falling object will reach.

• The terminal velocity depends on the size, shape, and mass of the falling object.