# Motion

## Describing Motion

An object is in motion when it changes position. When an object moves from one location to another, it is changing position in relation to a stationary point known as a reference point. Earth’s surface, or something attached to it, are common reference points. The Sun, other stars, and the planets can be used as reference points to describe motion in the solar system and the universe. Earth is in constant motion relative to the Sun.

### Speed

One measure of motion is speed, or the distance an object travels over time compared to a reference point. Speed can be calculated using the following equation.

Speed is always measured in a unit of distance per a unit of time, such as meters per second (m/s) or kilometers per hour (km/h). A falling rock, for example, might hit the ground at a speed of 10 m/s, while a car on the highway may travel at a speed of 100 km/h (about 60 mph).

### Velocity

If you know a car is traveling at 100 km/h, you still do not have enough information to completely describe its motion. Velocity is a measure of both the speed and direction of an object’s motion. If you have a compass in your car, you may be able to determine that your velocity is 100 km/h east. Meanwhile, the rock falling from a cliff is traveling at 10 mis downward.

Like speed, velocity is measured relative to some reference point. Because velocity includes a direction component, velocities can combine either by adding together or subtracting from each other. For example, suppose a train is moving east at 200 km/h relative to the ground. A passenger walks toward the front of the train at 4 km/h relative to the people seated on the train. The passenger’s overall velocity relative to the ground is 204 km/h east. As the same passenger walks back toward his seat at 4 km/h toward the back of the train, his overall velocity is 196 km/h east.

### Acceleration

In common language, to accelerate means to go faster. Press the accelerator pedal on a car, and the car’s speed increases. In physical science, however, an acceleration is the rate of change in velocity. Remember that velocity includes the speed and direction of an object. Therefore a change in velocity can be a change in either speed or direction. A car that is slowing down is accelerating in the opposite direction of its motion. This is sometimes called a deceleration. A moving object that changes direction is also undergoing an acceleration even if its speed does not change.

To determine the acceleration of an object, first calculate the change in velocity by subtracting the initial velocity from the final velocity. Then divide the change in velocity by the amount of time over which the change occurred.

If the direction of motion does not change, the change in velocity is the same as the change in speed. The change in velocity is then the final speed minus the initial speed. The change in velocity is a unit of speed, such as m/s. Therefore the unit of acceleration is a unit of speed divided by a unit of time. Time is commonly measured in seconds, so acceleration is usually measured in meters per second per second, or m/s2. If the direction of motion does not change, the change in velocity is the same as the change in speed. The change in velocity is then the final speed minus the initial speed. The change in velocity is a unit of speed, such as m/s. Therefore the unit of acceleration is a unit of speed divided by a unit of time. Time is commonly measured in seconds, so acceleration is usually measured in meters per second per second, or -3 m/s2.

1. A ball rolls 20 m across a parking lot in 4 s. What is the speed of the ball?
2. What does a horizontal line on a speed-time graph indicate about the acceleration of an object traveling in a straight line?

## Momentum

To understand momentum, we first need to understand the relationship between mass (the amount of matter in an object) and force (a push or pull exerted on an object). Imagine a person struggling to push a piano. Then imagine the person using the same force to push a small book, which has a much smaller mass than the piano. While the piano might barely move, the book would move easily. Momentum is the product of velocity and mass. A bullet is small, but it has great momentum when it travels at high speeds. A heavy truck, even one that moves slowly-also has great momentum.

### Calculating Momentum

Momentum is a property of a moving object that is equal to the mass of the object multiplied by the velocity of the object. Because velocity includes direction, momentum has a direction associated with it. An object’s momentum is in the direction of its velocity. Momentum can be calculated as follows.

If mass is measured in kilograms, and velocity in meters per second, momentum has units of kilogram-meters per second, or kg \times m/s. The greater the velocity of an object, the greater the object’s momentum. Consider, for example, a 12-kg bicycle at two different velocities.

The greater the mass of an object, the greater the object’s momentum. Consider a cart moving at a velocity of 2 m/s west. Bricks can be added to the cart to change its mass. The calculations below show how the cart’s momentum increases as its mass increases.

## Law of Conservation of Momentum

When two objects collide, one object’s momentum can be transferred to the other object. No momentum is created or lost in the process. The law of conservation of momentum states that if no other forces act on the objects, their total momentum remains the same after they interact.

## Collisions of Objects The amount of momentum that is transferred when two objects collide depends on the objects’ initial motion. In graphic A, both pucks are moving toward the right. They have the same mass, but the puck on the left is moving faster. Its momentum is greater than the momentum of the puck on the right. After they collide, both pucks will continue to move in the same direction. The puck on the right will speed up, and the puck on the left will slow down. The momentum of each puck will change, but the total momentum of both pucks will be the same as it was before the collision.

In graphic B, the pucks are moving at the same speed toward each other. As a result, their momentum is equal in magnitude but opposite in direction. After they collide, each reverses direction. They again travel at the same speed but in opposite directions. Thus, their total momentum is the same before and after the collision.

#### Elastic Collisions

In an elastic collision, there is no loss of kinetic energy in the collision. For example, in the collision shown in B, the pucks move away at the same speed but at opposite directions from their original motion. Momentum and kinetic energy are both conserved in an elastic collision. When objects larger than molecules collide, there is always some energy change, so the collision is not perfectly elastic.

#### Inelastic Collisions

Some of the kinetic energy is changed to another form of energy in an inelastic collision. In a completely inelastic collision, the two objects stick together after the collision. Any real-world collision between objects converts some of the kinetic energy into some other form of energy such as heat, sound, or the motion of particles inside the objects.

For example, a bicycle helmet protects the rider in an accident by transmitting the energy of a collision with the ground into the padding of the helmet. As the protective foam collapses, it absorbs energy. Without the helmet, much more of the energy of the collision is transferred to the rider’s head. Although energy is not conserved, momentum is conserved in an inelastic collision.