DTW GED PREP

Motion

You probably already know that speed describes how fast something is moving.

An object’s speed can be calculated using this equation:

Speed= distance/ time.  or v = d/ t

Note: Speed is often represented by a lowercase v because the same formula is used to calculate velocity.

Speed vs. Velocity

Velocity is speed in a specific direction.

Example: A car traveling at 40 miles per hour (mph) toward Location B has a velocity of +40 mph. The same car returning toward Location A at the same speed has a velocity of −40 mph. Although speed remains the same (40 mph), velocity changes because the direction changes.

Acceleration

When an object speeds up, slows down, or changes direction, it is accelerating. Acceleration describes any change in an object’s velocity. You can calculate acceleration with the following equation:

acceleration= final velocity – original velocity / time.    or    a = v2 – v1/t

Momentum and Collisions

When an object is moving, the product of its mass and velocity is called its momentum.

The momentum equation is: momentum= mass x velocity.  or p = m x v

The larger an object’s mass and the faster it moves, the greater its momentum.

Momentum Transfer in Collisions: When objects collide, they transfer momentum to each other. Example: Two cars colliding may change velocity. Their masses remain the same, but their velocities change because they transfer momentum during impact.

Law of Conservation of Momentum: The total combined momentum of the two objects remains the same before and after a collision.

Like energy, momentum cannot be created or destroyed—it can only be transferred between objects.

Inertia: Inertia is the tendency of an object to resist changes in its motion. Objects at rest tend to stay at rest. Objects in motion tend to stay in motion.

 Example: When a moving car stops suddenly, the people inside continue moving forward because of inertia.

Seat belts and airbags are safety features designed to reduce injuries by slowing down the occupants safely, preventing them from being thrown forward.

Force

A force is any push or pull applied to an object. All objects exert forces on one another.

Most objects experience multiple forces at the same time.

Balanced and Unbalanced Forces: Balanced forces cancel each other out and do not cause motion to change. Unbalanced forces do cause a change in motion. They make objects accelerate, which includes: Speeding up, Slowing down, Changing direction

 Example:Imagine two dogs pulling opposite ends of a rope: If both dogs pull with equal force, the forces are balanced, and the rope doesn’t move. If one dog pulls harder, the forces are unbalanced, and the rope accelerates toward the stronger dog.

Newton’s Laws of Motion

In the late 1600s, Sir Isaac Newton developed three laws of motion that explain how forces affect the movement of objects. These laws are still used today to describe all motion on Earth and in space.

Law, Description and Example

• First Law (Inertia) An object at rest stays at rest, and an object in motion stays in motion unless acted on by an unbalanced force. Example: A skateboard keeps rolling until friction or another force stops it.
• Second Law (F = ma) The force on an object equals its mass times its acceleration.            A heavier skateboard requires more force to accelerate.
• Third Law (Action–Reaction) For every action, there is an equal and opposite reaction.      When you push the ground with your foot, the ground pushes back and moves the skateboard forward.

Gravity

Newton also formulated the law of universal gravitation, which states: Every object in the universe attracts every other object with a force called gravity. This gravitational force depends on two factors: The masses of the objects The distance between them

> Diagram Note: The strength of gravity increases with greater mass and decreases with greater distance.

Effects of Gravity

Gravity explains why: The moon orbits Earth; Earth orbits the Sun; Objects fall to the ground when dropped

 Earth has a large mass and we’re very close to it, so its gravitational force on us is very strong.

• Free Fall

An object is in free fall when gravity is the only force acting on it.

On Earth, true free fall rarely happens because of air resistance.

In free fall, objects accelerate toward Earth at a constant rate of: 9.8 m/s^2

Mass and Weight

Though often confused, mass and weight are not the same:

Mass                                                                         Weight

The amount of matter in an object         The gravitational force acting on that mass

Measured in kilograms (kg)                      Measured in newtons (N) or pounds (lb)

Does not change with location                  Changes depending on gravity

Example:

If your weight on Earth is 170 pounds, your weight on the Moon would be about 28 pounds due to lower gravity. However, your mass remains the same in both places.

Work and Machines

Consider two boxes: One is empty; The other is full of books.

You can easily push the empty box across the floor. But no matter how hard you push the full box, it doesn’t move.

Key Idea: In science, work only happens when a force causes an object to move a distance. You exerted force on both boxes.Only the empty box moved. Therefore, you did work only on the empty box. Even if you exerted more force trying to move the full box, no work was done because it didn’t move.

Calculating Work; The amount of work done on an object is calculated by:

work  = force x distance.     or   w = F x d

Simple Machines

Simple machines help make work easier. They usually reduce the applied force needed, but require more distance. In other words, you trade force for distance.

The Six Types of Simple Machines:

• Inclined plane, Wedge Screw, Lever, Wheel and axle, Pulley

How Simple Machines Help

Simple machines do not reduce the total amount of work. Instead, they can:

Reduce the force you need to apply, and Change the direction of the force

 Example: A screw moves downward as you turn it clockwise. Turning it is easier than pushing it straight in.

As you push down with an axe (a wedge), it pushes out to split wood. It is easier to swing an axe downward than to pull wood apart with your hands.

Mechanical Advantage

When a machine amplifies force, it gives you mechanical advantage. If the output force is greater than the input force, the machine amplifies the force. Mechanical advantage describes how much the machine multiplies your force.

Key Principle:  w = F x d

 Simple machines cannot reduce the total work done. If you reduce the input force, you must increase the distance.

Example: Ramp vs. Lifting: Lifting a box straight up = shorter distance, more force.

Using a ramp = longer distance, less force.

Power

Power is the amount of work done in a certain amount of time. The faster a machine performs work, the greater its power.

Power Equation: power = work ÷ time.   or      P = w÷t

In summary: Work = force × distance. Machines help by reducing input force over greater distance. Mechanical advantage = amplifying force Power = work divided by time