What you'll learn
Why does a car need seat belts? Why does a ramp make lifting easier? These are questions about forces and motion. In this lesson you will learn to:
- describe motion with speed, velocity and acceleration, and read distance-time graphs;
- apply Newton's three laws of motion;
- understand momentum and gravity (including the difference between mass and weight);
- calculate work and power;
- explain how simple machines give mechanical advantage.
How it shows up on the GED: Motion and forces is one of three physical science topics, which together make up about 40% of the Science test. Questions use short experiment descriptions, force diagrams, distance-time graphs and data tables. Many are short calculations with a formula such as v = \dfrac{d}{t}, F = ma or W = Fd. On the GED, the formula you need is usually given in the question or on a reference sheet, so your job is to pick the right numbers and plug them in.
Key terms
- force — a push or pull, measured in newtons (N).
- net force — the total of all forces on an object, with opposite directions subtracted (20 N right and 5 N left = 15 N right).
- speed — distance traveled per unit of time (60 miles per hour).
- velocity — speed in a given direction (60 mph north).
- acceleration — the rate at which velocity changes: speeding up, slowing down or turning.
- inertia — an object's tendency to keep doing what it is doing; more mass = more inertia.
- friction — a force that opposes motion between surfaces in contact.
- momentum — mass times velocity (a slow truck can have more momentum than a fast bike).
- gravity — the attractive force between all masses; on Earth it pulls objects down at 9.8 m/s².
- mass — the amount of matter in an object, in kilograms; the same everywhere.
- weight — the force of gravity on an object, in newtons; changes from planet to planet.
- work — force times the distance moved in the direction of the force, in joules (J).
- power — how fast work is done, in watts (W); 1 W = 1 J per second.
- simple machine — a device that changes the size or direction of a force (lever, ramp, pulley).
- mechanical advantage — how many times a machine multiplies the input force.
Describing motion: speed, velocity and acceleration
Speed tells how fast something moves: v = \dfrac{d}{t}. A runner who covers 400 m in 80 s has an average speed of 400 \div 80 = 5 m/s. Velocity is speed plus direction, so two cars both going 50 mph, one north and one south, have the same speed but different velocities.
Average speed for a whole trip is total distance ÷ total time, including stops. If you drive 60 miles in 1 hour, stop for 1 hour, then drive 60 more miles in 1 hour, your average speed is 120 \div 3 = 40 mph, not 60.
Acceleration is how quickly velocity changes: a = \dfrac{v_f - v_i}{t} (v_f = final velocity, v_i = starting velocity). A car going from 0 to 20 m/s in 5 s accelerates \dfrac{20 - 0}{5} = 4 m/s². Slowing down and turning are also acceleration.
Reading distance-time graphs:
- Flat line → distance is not changing → the object is at rest.
- Straight sloped line → constant speed. A steeper line = faster.
- Curve getting steeper → speeding up (accelerating).
- Speed of a straight segment = rise ÷ run = change in distance ÷ change in time.
Read the axis labels: on a speed-time graph, a flat line means constant speed.
Newton's three laws of motion
First law (inertia): An object at rest stays at rest, and an object in motion keeps moving at the same speed and direction, unless a net force acts on it. When a car stops suddenly, your body keeps moving forward; the seat belt supplies the force that stops you.
Second law (F = ma): The acceleration of an object depends on the net force and the mass. More force → more acceleration. More mass → less acceleration for the same force. Pushing an empty cart (small mass) with the same force as a full cart (large mass) makes the empty cart speed up faster. If a 1,000 kg car has a net force of 2,000 N, then a = \dfrac{F}{m} = \dfrac{2{,}000}{1{,}000} = 2 m/s².
Third law (action–reaction): For every action force there is an equal and opposite reaction force. Forces always come in pairs acting on two different objects. A swimmer pushes water backward; the water pushes the swimmer forward. A rocket pushes hot gas down; the gas pushes the rocket up. Because the pair acts on different objects, the forces do not cancel each other out.
Net force: add forces in the same direction; subtract opposite forces. If the net force is zero, motion does not change.
Momentum and gravity
Momentum (p = mv) is "mass in motion." A 2,000 kg truck at 10 m/s has momentum 2{,}000 \times 10 = 20{,}000 kg·m/s. A 1,000 kg car at 15 m/s has 15{,}000 kg·m/s. The truck has more momentum even though it is slower, which is why it is harder to stop.
In a collision with no outside forces, total momentum is conserved: total before = total after. If a moving cart sticks to a resting cart, the pair moves off more slowly, because the same momentum is now shared by more mass.
Gravity is a force of attraction between any two masses. It gets stronger with more mass and weaker with more distance. Earth's large mass pulls everything near its surface toward its center.
Near Earth's surface, falling objects (ignoring air resistance) speed up by about 9.8 m/s every second.
Mass vs. weight: Mass is the amount of matter (kg) and does not change with location. Weight is the pull of gravity on that mass: weight = mg, in newtons. A 60 kg person weighs 60 \times 9.8 = 588 N on Earth. On the Moon, where gravity is about one-sixth as strong, the same person still has a mass of 60 kg but weighs only about 98 N.
Work, power and simple machines
In science, work is done only when a force moves something in the direction of the force: W = Fd. Lifting a 100 N box 2 m does 100 \times 2 = 200 J of work. Pushing hard on a wall that does not move does no work (distance = 0), even though you get tired.
Power is the rate of doing work: P = \dfrac{W}{t}. If one person lifts the box in 2 s and another in 4 s, they do the same 200 J of work, but the first uses 200 \div 2 = 100 W of power and the second 200 \div 4 = 50 W.
Simple machines make work easier by changing the size or direction of a force. They never reduce the total work (and friction makes the work slightly larger). The trade-off: less force means more distance.
| Machine | How it helps | Example |
|---|---|---|
| Lever | Long effort arm, short load arm | Crowbar, seesaw, bottle opener |
| Inclined plane (ramp) | Push along a longer slope instead of lifting straight up | Wheelchair ramp |
| Pulley | Changes direction; several pulleys reduce force | Flagpole, crane |
| Wheel and axle | Small force on big wheel turns axle with big force | Doorknob, steering wheel |
| Wedge / screw | Turns a push into a splitting or squeezing force | Axe, jar lid |
Mechanical advantage (MA) = output force ÷ input force. For a lever, MA = effort arm ÷ load arm. For a ramp, MA = ramp length ÷ height. An MA of 4 means you push with one-fourth of the force, but over four times the distance.
Formulas you may see
On the GED, the formula you need is usually given in the question or on a reference sheet, so your job is to pick the right numbers and plug them in.
| Quantity | Formula | Units |
|---|---|---|
| Speed | v = \dfrac{d}{t} | m/s, km/h, mph |
| Acceleration | a = \dfrac{v_f - v_i}{t} | m/s² |
| Newton's second law | F = ma | N = kg·m/s² |
| Weight | weight = mg, g = 9.8 m/s² | N |
| Momentum | p = mv | kg·m/s |
| Work | W = Fd | J = N·m |
| Power | P = \dfrac{W}{t} | W = J/s |
| Mechanical advantage | MA = \dfrac{F_{\text{out}}}{F_{\text{in}}} | no units |
Rearrange as needed: a = \dfrac{F}{m}, d = vt.
Worked example 1: Average speed from a table
Passage: A delivery van's trip log shows three parts.
| Part | Distance (km) | Time (h) |
|---|---|---|
| Highway | 90 | 1.0 |
| Lunch stop | 0 | 0.5 |
| City streets | 30 | 1.0 |
Question: What was the van's average speed for the whole trip?
A. 40 km/h B. 48 km/h C. 60 km/h D. 90 km/h
Think-aloud:
- Average speed = total distance ÷ total time, so add everything, including the stop.
- Total distance: 90 + 0 + 30 = 120 km. Total time: 1.0 + 0.5 + 1.0 = 2.5 h.
- v = \dfrac{120}{2.5} = 48 km/h. That is B.
- Traps: 60 km/h ignores the stop; 90 km/h is the highway speed only; 40 km/h averages the three speeds.
Answer: B (48 km/h)
Worked example 2: Which law of motion?
Passage: A bus driver brakes hard. Standing passengers lurch forward, even though nothing pushed them forward.
Question: Which idea best explains why the passengers lurch forward?
A. Every action has an equal and opposite reaction. B. Objects in motion tend to stay in motion unless a force acts on them. C. Acceleration equals force divided by mass. D. Gravity pulls the passengers toward the front of the bus.
Think-aloud:
- Before braking, the passengers were moving forward with the bus.
- The brakes stop the bus, but no force acts directly on the passengers' bodies at first, so their bodies keep moving forward. That is inertia, Newton's first law: B.
- A is about force pairs; C does not explain why they keep moving; D is wrong because gravity pulls down.
Answer: B
Worked example 3: Using F = ma
Passage: An engineer tests a 1,200 kg car. On a level road it speeds up from 0 to 18 m/s in 6.0 s. Use a = \dfrac{v_f - v_i}{t} and F = ma.
Question: What net force acted on the car?
Think-aloud:
- Two formulas are given, so this is a two-step problem: find a first, then F.
- Acceleration: a = \dfrac{18 - 0}{6.0} = 3.0 m/s².
- Net force: F = ma = 1{,}200 \times 3.0 = 3{,}600 N.
- Trap: multiplying the mass by the speed (1{,}200 \times 18 = 21{,}600) gives momentum, not force. Check units: kg × m/s² = N. ✓
Answer: 3,600 N
Worked example 4: Ramps, work and mechanical advantage
Passage: A mover must raise a 600 N appliance onto a truck bed 1.0 m high. Option 1: lift it straight up. Option 2: push it up a 4.0 m ramp, which takes a force of 150 N (ignore friction). Use W = Fd.
Question: Which statement is correct?
A. The ramp reduces both the force and the work. B. The ramp reduces the force, but the work is the same. C. The ramp increases the force but reduces the work. D. Lifting straight up takes less force than using the ramp.
Think-aloud:
- Work lifting straight up: W = 600 \times 1.0 = 600 J.
- Work using the ramp: W = 150 \times 4.0 = 600 J. Same work!
- The force dropped from 600 N to 150 N, but the distance grew from 1.0 m to 4.0 m. That is B.
- MA of the ramp = \dfrac{600}{150} = 4, which also equals \dfrac{4.0\text{ m}}{1.0\text{ m}}.
- A is the classic trap: machines never reduce work.
Answer: B
Common mistakes
- Leaving out stops when finding average speed. Wrong: average the moving parts only. Right: total distance ÷ total time, including time spent stopped.
- Thinking a moving object needs a force to keep moving. Wrong: a sliding box stops because "its force runs out." Right: friction (an outside force) slows it; with no friction it would keep going (first law).
- Adding forces that point in opposite directions. Wrong: 50 N right + 20 N left = 70 N. Right: subtract opposite forces: net force = 30 N right.
- Confusing mass and weight. Wrong: an astronaut has less mass on the Moon. Right: mass stays the same; only weight (the pull of gravity) changes.
- Believing machines save work. Wrong: a lever reduces the work you do. Right: it reduces the force but increases the distance; work stays the same (or grows slightly with friction).
- Mixing up formulas. Wrong: using p = mv when asked for force. Right: check the units the question wants; newtons = F = ma, joules = W = Fd, watts = P = \dfrac{W}{t}.
GED test strategy
- Find the formula in the question first. Then write down each value with its unit and match it to a letter.
- Sketch force arrows: same direction add; opposite directions subtract.
- Read graph axes first: distance or speed? Seconds or minutes?
- Use units as a check. If the answer should be in newtons and your number came from kg × m/s, you used the wrong formula.
- Eliminate choices that break laws: machines that reduce work, forces without pairs, mass that changes on the Moon.
- For two-step problems, name both steps before you start.
Calculator tip (TI-30XS)
For a two-step problem such as net force then acceleration, use parentheses so you only press enter once: ( 50 − 20 ) ÷ 15 enter gives 2. For average speed with several parts, add the parts inside parentheses on top and bottom: ( 300 + 0 + 500 + 200 ) ÷ ( 100 + 50 + 250 + 100 ) enter gives 2.
Check yourself
A Bike Ride to the Store
Marcus rode his bike in a straight line from his home toward a store. A fitness app on his phone recorded his distance from home every few seconds. The graph shows his trip, which has four parts, labeled A through D.
On a distance-time graph, the slope (steepness) of the line shows speed. A steeper line means a greater speed, and a flat line means the object is not moving. Average speed is found by dividing the distance traveled by the time it took.
During which part of the trip was Marcus not moving?
Hint
What does the line look like when the distance from home stays the same?
Step-by-step solution
Evidence: The passage says "a flat line means the object is not moving." On the graph, segment B is flat: Marcus stays 300 m from home from 100 s to 200 s.
Step by step:
- Moving means the distance from home is changing.
- Segment A rises from 0 m to 300 m, segment C rises from 300 m to 800 m, and segment D rises from 800 m to 1,000 m. In all three, the distance changes, so he is moving.
- In segment B the distance stays at 300 m for 100 seconds. Time passes but distance does not change, so he is at rest (maybe waiting at a traffic light).
The answer is segment B.
Tip: On a distance-time graph, a horizontal line means "stopped." Do not confuse it with a speed-time graph, where a horizontal line means steady speed.
Check yourself
A Bike Ride to the Store
Marcus rode his bike in a straight line from his home toward a store. A fitness app on his phone recorded his distance from home every few seconds. The graph shows his trip, which has four parts, labeled A through D.
On a distance-time graph, the slope (steepness) of the line shows speed. A steeper line means a greater speed, and a flat line means the object is not moving. Average speed is found by dividing the distance traveled by the time it took.
Using the graph and the formula v = \dfrac{d}{t}, what was Marcus's speed during part A of the trip?
m/s
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Read how far he traveled during part A and how many seconds part A lasted.
Step-by-step solution
Evidence: Segment A on the graph runs from (0 s, 0 m) to (100 s, 300 m). The passage says average speed is "found by dividing the distance traveled by the time it took."
Step by step:
- Distance during A: 300 - 0 = 300 m.
- Time during A: 100 - 0 = 100 s.
- Speed: v = \frac{d}{t} = \frac{300\text{ m}}{100\text{ s}} = 3\text{ m/s}
- Check: at 3 m/s for 100 s, he would go 3 \times 100 = 300 m. ✓
His speed during part A was 3 m/s.
Tip: For a straight segment, speed = change in distance ÷ change in time. Subtract the starting values from the ending values on each axis before dividing.
Summary
- Speed = \dfrac{d}{t}; average speed uses total distance and total time, including stops. Acceleration is any change in velocity.
- On a distance-time graph, flat = at rest and steeper = faster. Speed = change in distance ÷ change in time.
- Newton's laws: (1) objects keep doing what they are doing unless a net force acts; (2) F = ma; (3) forces come in equal and opposite pairs acting on different objects.
- Momentum p = mv is conserved in collisions. Weight = mg changes with gravity; mass does not.
- Work W = Fd needs motion in the direction of the force; power P = \dfrac{W}{t}. Simple machines trade a smaller force for a longer distance; they never reduce work.