GACE Middle Grades Science (4–8) (705)

Motion is change in position over time. Position describes location relative to a reference point. Displacement is the change in position, including direction.

Distance is the total path length traveled. Displacement is the straight-line distance from start to finish with direction. A round trip has distance but zero displacement.

Velocity is displacement divided by time. Velocity includes both magnitude and direction. Velocity is a vector quantity. An object moving in a circle at constant speed has changing velocity because direction changes.

Acceleration is the rate of change of velocity. Acceleration occurs when speed changes, direction changes, or both change. Acceleration is also a vector quantity.

Positive acceleration means velocity is increasing. Negative acceleration (deceleration) means velocity is decreasing. An object thrown upward experiences negative acceleration due to gravity throughout its flight.

Position-time graphs show location versus time. A horizontal line indicates the object is stationary. A straight diagonal line indicates constant velocity. A curved line indicates acceleration.

The slope of a position-time graph equals velocity. Steeper slopes indicate greater speeds. Positive slopes indicate motion in the positive direction. Negative slopes indicate motion in the negative direction.

Velocity-time graphs show velocity versus time. A horizontal line indicates constant velocity. A diagonal line indicates constant acceleration.

The slope of a velocity-time graph equals acceleration. The area under the curve equals displacement. A line above the time axis indicates positive velocity; below indicates negative velocity.

Newton's First Law (Law of Inertia) states that an object at rest stays at rest and an object in motion stays in motion at constant velocity unless acted upon by an unbalanced force.

Inertia is the tendency of objects to resist changes in motion. Mass is a measure of inertia. More massive objects are harder to accelerate or decelerate.

Newton's Second Law states that acceleration is directly proportional to net force and inversely proportional to mass. The equation is F = ma. Force is measured in newtons (N). One newton accelerates one kilogram at one meter per second squared.

Doubling the force doubles the acceleration. Doubling the mass halves the acceleration. This law explains why heavy objects require more force to move.

Newton's Third Law states that for every action there is an equal and opposite reaction. Forces always occur in pairs. When you push on a wall, the wall pushes back on you with equal force.

Gravity is the attraction between all objects with mass. Gravitational force increases with mass and decreases with distance. On Earth's surface, gravitational acceleration is approximately 9.8 m/s².

Weight is the gravitational force on an object. Weight equals mass times gravitational acceleration (W = mg). Weight varies with location; mass does not.

Friction opposes motion between surfaces in contact. Static friction prevents stationary objects from moving. Kinetic friction acts on moving objects. Friction converts kinetic energy to thermal energy.

Friction depends on surface roughness and normal force. Friction does not depend on contact area or speed. Lubricants reduce friction by separating surfaces.

Normal force is perpendicular to a surface. For an object on a horizontal surface, normal force equals weight. On an incline, normal force equals the component of weight perpendicular to the surface.

Tension is the pulling force transmitted through a string, rope, or cable. Tension is the same throughout an ideal massless rope.

Applied force is any push or pull exerted by an object or person. Applied forces can act in any direction.

Air resistance is friction between moving objects and air. Air resistance increases with speed and surface area. Terminal velocity occurs when air resistance equals weight, resulting in zero net force and constant velocity.

Balanced forces are equal in magnitude and opposite in direction. They produce no acceleration. An object with balanced forces is in equilibrium, either at rest or moving at constant velocity.

Unbalanced forces produce acceleration in the direction of the net force. Net force is the vector sum of all forces acting on an object.

Free body diagrams show all forces acting on an object as arrows. Arrow length represents force magnitude. Arrow direction represents force direction. The object is represented as a point or simple shape.

Work occurs when a force causes displacement in the direction of the force. Work equals force times displacement times the cosine of the angle between them. Work is measured in joules (J).

No work is done if there is no displacement. No work is done if force is perpendicular to displacement. Carrying a box horizontally does no work against gravity because displacement is perpendicular to gravitational force.

Kinetic energy is energy of motion. Kinetic energy equals one-half times mass times velocity squared (KE = ½mv²). Doubling velocity quadruples kinetic energy.

Potential energy is stored energy due to position or condition. Gravitational potential energy equals mass times gravitational acceleration times height (PE = mgh). Height is measured from a reference point.

Elastic potential energy is stored in stretched or compressed elastic materials. Springs and rubber bands store elastic potential energy.

Mechanical energy is the sum of kinetic and potential energy. In the absence of friction, mechanical energy is conserved. As potential energy decreases, kinetic energy increases by the same amount.

The law of conservation of energy states that energy cannot be created or destroyed, only transformed. Total energy in an isolated system remains constant. When mechanical energy appears to be lost, it has been converted to other forms such as thermal energy.

Power is the rate of doing work. Power equals work divided by time. Power is measured in watts (W). One watt equals one joule per second. Higher power means doing the same work in less time.

Simple machines reduce the force needed to do work by increasing the distance over which force is applied. They do not reduce the amount of work required.

Mechanical advantage is the ratio of output force to input force. Ideal mechanical advantage ignores friction. Actual mechanical advantage accounts for energy losses.

Levers consist of a rigid bar rotating around a fulcrum. First-class levers have the fulcrum between the effort and load (seesaw). Second-class levers have the load between the fulcrum and effort (wheelbarrow). Third-class levers have the effort between the fulcrum and load (fishing rod).

Pulleys redirect force and can provide mechanical advantage. A single fixed pulley changes direction but provides no mechanical advantage. Movable pulleys and pulley systems increase mechanical advantage.

Inclined planes reduce the force needed to raise an object by increasing the distance traveled. A longer, gentler ramp requires less force than a short, steep ramp.

Wedges are moving inclined planes that separate or hold objects. Axes, knives, and doorstops are wedges.

Screws are inclined planes wrapped around a cylinder. Screws convert rotational motion to linear motion. Tighter thread spacing provides greater mechanical advantage.

Wheels and axles consist of two cylinders of different diameters rotating together. The wheel has larger diameter than the axle. Force applied to the wheel produces greater force at the axle.

Thermal energy is the total kinetic energy of particles in a substance. Temperature is the average kinetic energy of particles. Higher temperature means faster particle motion.

Heat is the transfer of thermal energy from warmer objects to cooler objects. Heat flows spontaneously from high temperature to low temperature.

Conduction transfers heat through direct contact. Particles collide and transfer kinetic energy. Metals are good conductors; gases are poor conductors.

Convection transfers heat through fluid movement. Warm fluid rises; cool fluid sinks. Convection currents distribute heat throughout fluids.

Insulators reduce heat transfer. Air, foam, and fiberglass trap air pockets that resist conduction. Shiny surfaces reflect radiation.

Specific heat capacity is the amount of energy needed to raise one gram of a substance by one degree Celsius. Water has high specific heat, meaning it resists temperature change. This property moderates coastal climates.

Phase changes involve energy transfer without temperature change. Melting and vaporization absorb energy. Freezing and condensation release energy.