Science Physics Grade 9 Motion Uniform and Non-uniform

Study Guide: Motion – Uniform and Non-Uniform
Grade 9, Physics (NGSS-aligned)

1. The Driving Question

If you’re driving at 60 mph on the highway and suddenly hit the brakes, why does your speedometer drop smoothly but your stomach lurches forward like it’s trying to escape? And how can two cars moving at the same speed feel totally different—one like a smooth glide, the other like a rollercoaster?

2. The Core Idea – Built, Not Listed

Imagine you’re on a skateboard at the top of a hill. You push off once and coast down—your speed increases the whole way. That’s non-uniform motion: your velocity changes because of gravity pulling you faster. Now imagine you’re on a moving walkway at the airport. You stand still, but the walkway carries you forward at a constant 2 mph. That’s uniform motion: your velocity stays the same because nothing’s pushing or pulling you differently.

Motion isn’t just about how fast you’re going—it’s about how that speed changes (or doesn’t). A car cruising at 55 mph on a flat highway is in uniform motion, but the same car swerving through city traffic is non-uniform because it speeds up, slows down, and turns. The key difference? Acceleration—any change in velocity, whether speeding up, slowing down, or changing direction.

Key Vocabulary:
- Velocity: Speed and direction. Example: A plane flying 500 mph north has velocity; a plane flying 500 mph in circles has speed but no constant velocity.
- Acceleration: How quickly velocity changes. Example: A subway train that goes from 0 to 30 mph in 10 seconds has an acceleration of 3 mph per second.
- College note: In calculus-based physics, acceleration is the derivative of velocity—meaning it’s the instantaneous rate of change, not just an average.
- Uniform motion: Motion with constant velocity (no acceleration). Example: A satellite orbiting Earth at a steady 17,500 mph is in uniform motion because its speed and direction don’t change.
- Non-uniform motion: Motion with changing velocity (acceleration present). Example: A basketball bouncing—it speeds up as it falls, slows down when it hits the ground, and changes direction.

3. Assessment Translation

How this appears on assessments:
- Multiple choice: Questions often show a position-time or velocity-time graph and ask, "Which segment shows uniform motion?" or "Where is the object accelerating?" - Distractor patterns: Confusing speed with velocity (e.g., "constant speed" vs. "constant velocity"), or misreading graphs (e.g., thinking a flat line on a position-time graph means the object is stopped, when it actually means constant velocity).
- Short answer: "A car travels 100 meters in 5 seconds, then 100 meters in 3 seconds. Is this uniform or non-uniform motion? Explain using velocity." - Proficient response: "Non-uniform. The car’s velocity changes from 20 m/s (100m/5s) to ~33 m/s (100m/3s), so it’s accelerating." - Developing response: "Non-uniform because it goes faster." (Lacks calculation and velocity definition.) - Graph interpretation: "The graph below shows a runner’s position over time. Describe their motion in each segment." - What teachers look for: Correctly identifying flat lines (uniform motion), straight slopes (constant velocity), and curved lines (acceleration).

Model Proficient Response (Short Answer):
Prompt: "A cyclist rides 30 meters in 6 seconds, stops for 4 seconds, then rides another 30 meters in 5 seconds. Is this uniform or non-uniform motion? Justify with calculations." Response: "The motion is non-uniform. From 0–6 seconds, the cyclist’s velocity is 5 m/s (30m/6s). From 6–10 seconds, velocity is 0 m/s (stopped). From 10–15 seconds, velocity is 6 m/s (30m/5s). Since velocity changes, this is non-uniform motion. The stop also counts as acceleration (deceleration to 0)."

4. Mistake Taxonomy

Mistake 1: Confusing speed and velocity
- Prompt: "A race car drives 5 laps around a 1-mile track at 100 mph. Is its velocity constant? Explain." - Common wrong answer: "Yes, because its speed is constant." - Why it loses credit: Velocity includes direction. The car’s direction changes every lap, so velocity isn’t constant.
- Correct approach: "No. Velocity is speed and direction. The car’s direction changes as it turns, so its velocity isn’t constant—even though its speed is."

Mistake 2: Misreading position-time graphs
- Prompt: "The graph shows a car’s position over time. During which segment is the car moving fastest?" (Graph has three segments: steep slope, flat line, gentle slope.) - Common wrong answer: "The flat line, because it’s not moving." - Why it loses credit: Flat line = no motion (velocity = 0). Steeper slope = faster velocity.
- Correct approach: "The steepest slope. On a position-time graph, steeper lines mean higher velocity."

Mistake 3: Ignoring direction in acceleration
- Prompt: "A ball is thrown straight up. Is it accelerating on the way up? Explain." - Common wrong answer: "No, because it’s slowing down." - Why it loses credit: Acceleration is any change in velocity—including slowing down or changing direction. Gravity is still acting on the ball.
- Correct approach: "Yes. Gravity causes the ball to decelerate (negative acceleration) on the way up, but it’s still accelerating because its velocity is changing."

5. Connection Layer

• Within physics: Uniform motion → Newton’s First Law — Objects in uniform motion stay that way unless acted on by a force. A hockey puck sliding on ice (low friction) approximates uniform motion.
• Across subjects: Non-uniform motion → Calculus (derivatives) — The slope of a position-time graph is velocity; the slope of a velocity-time graph is acceleration. This is how calculus describes motion mathematically.
• Outside school: Uniform vs. non-uniform motion → Video game design — In games like Mario Kart, uniform motion (constant speed on straightaways) feels smooth, while non-uniform motion (sharp turns, boosts) creates excitement. Designers tweak acceleration to make gameplay feel "right."

6. The Stretch Question

If you’re in a car moving at a constant 60 mph (uniform motion), and you drop a ball inside the car, where does it land? Now imagine the car is accelerating forward at 5 mph/s—where does the ball land now? Why does the same action feel different in the two scenarios?

Pointer toward the answer: In the first case, the ball lands at your feet because it’s already moving at 60 mph with you (Newton’s First Law). In the second case, the ball lands behind you because the car speeds up while the ball (briefly) keeps its original velocity. This is why you feel "pushed back" into your seat when a car accelerates—your body resists the change in motion (inertia). The same physics explains why rollercoasters feel more intense during drops and turns than during straightaways.