Constant Acceleration

Ever wondered why your speed changes when you're cycling downhill? That's acceleration in action - it's simply how quickly your velocity changes over time. Velocity itself is just how fast your displacement (position) changes.

You've got four key equations to master, and they're your best mates for solving motion problems. The most useful ones are v = u + at $final velocity = initial + acceleration × time$ and s = ut + ½at² (displacement with constant acceleration).

These equations work perfectly when acceleration stays constant. Think of a car speeding up at a steady rate - that's constant acceleration, and these formulas will tell you exactly where it'll be and how fast it's going at any moment.

Top Tip: Always write down what you know (u, v, a, s, t) before picking which equation to use!

Acceleration Due to Gravity

Drop anything right now and watch it fall - that's gravity pulling it down at roughly 9.81 m/s². When only gravity acts on an object (no air resistance), we call this free fall.

Free fall happens when gravity is the only force acting on an object. The ball you dropped? It's in free fall until air resistance becomes significant or it hits the ground.

Here's the clever bit: you can use all the same motion equations, but acceleration a always equals g = -9.81 m/s². The negative sign shows gravity pulls downward.

Remember: In free fall problems, gravity is your acceleration, and it's always pointing down!

Three Types of Gravitational Motion

Case 1: Dropping objects $u = 0$ - Start from rest and let gravity do the work. Your equations become super simple: v = gt, s = ½gt².

Case 2: Throwing upward - Use normal motion equations but remember a = g = -9.81. The object slows down, stops, then speeds up falling back down.

Case 3: Throwing downward - Again, normal equations with a = g = -9.81, but now initial velocity helps gravity pull the object down faster.

The key insight? Gravity always works the same way regardless of how the motion starts. Whether you drop, throw up, or throw down, that -9.81 m/s² is always there.

Quick Check: At the highest point of any upward throw, velocity = 0, but acceleration still equals -9.81 m/s²!

Practical: Measuring g Using Free Fall

This experiment lets you find g yourself using simple equipment. You'll drop a ball bearing from measured heights and time how long it takes to fall.

Set up an electromagnet to hold the ball, then release it whilst starting a timer simultaneously. When the ball hits a trapdoor, the circuit breaks and stops the timer. Measure the height h and time t, then repeat three times for accuracy.

Calculate g using g = 2h/t² $rearranged from s = ½gt²$. Do this for several different heights, then average your results. You should get close to 9.81 m/s²!

The electromagnet eliminates human error from releasing by hand, whilst the heavy ball bearing minimises air resistance effects.

Pro Tip: Plot a graph of height vs time² - the gradient × 2 gives you g!

Reducing Experimental Errors

Smart equipment choices make massive differences to your results. A small, heavy ball bearing means air resistance becomes negligible compared to gravity.

Using an electromagnet instead of dropping by hand removes the uncertainty from your release timing. Human reaction times are inconsistent, but electromagnetic releases are precise.

Repeating measurements three times and averaging reduces random errors. If one measurement goes wrong, the others balance it out.

When drawing experimental setups, always start with a clear diagram showing the key components and how they connect.

Error Reduction: Heavy + small object = less air resistance = more accurate results!

Projectile Motion

Think of a football being kicked - it moves forward and curves downward simultaneously. That's projectile motion, where horizontal and vertical movements are completely independent.

Horizontal component $VH = v cos θ$ stays constant because gravity doesn't affect sideways motion. Vertical component $VV = v sin θ$ changes due to gravity pulling downward.

The brilliant thing? Both components take the same time to complete their motion. The ball lands when the vertical motion finishes, regardless of horizontal speed.

For horizontal motion, use simple speed = distance/time. For vertical motion, use the gravity equations from earlier pages.

Key Insight: Horizontal and vertical motions are independent - solve them separately then combine!

Displacement-Time Graphs

Gradient equals velocity on displacement-time graphs - steeper slopes mean faster motion. When the line curves, acceleration is happening.

Bigger acceleration creates tighter curves because the gradient changes more rapidly. Smaller acceleration gives gentler curves with gradual gradient changes.

A straight line means constant velocity (no acceleration). Curves show changing velocity, and you can find instantaneous velocity by drawing tangents to the curve.

The mathematical relationship is simple: velocity = Δs/Δt, which is just the gradient of your displacement-time graph.

Graph Reading: Steep = fast, curved = accelerating, straight = constant velocity!

Velocity-Time Graphs

Bouncing balls create fascinating velocity-time graphs with sharp direction changes. When a ball bounces, its velocity sign flips instantly - downward motion becomes upward motion.

Vertical straight lines show the exact moments when the ball hits the floor and bounces. The velocity changes direction immediately.

Points where velocity equals zero represent the top of each bounce, where the ball momentarily stops before falling again.

These graphs clearly show how gravity continuously acts on the ball, even during the brief contact with the ground.

Bouncing Ball: Velocity changes sign at each bounce, but gravity never stops pulling downward!

Non-Uniform Acceleration

Real-world motion often involves changing acceleration - think of a car accelerating hard initially, then easing off. This creates curved lines on velocity-time graphs instead of straight ones.

Increasing acceleration appears as an increasingly steep gradient - the curve gets steeper with time. Decreasing acceleration shows the opposite - a curve that gradually flattens out.

Unlike constant acceleration, you can't use simple equations here. The changing gradient tells you acceleration is varying continuously.

These situations need more advanced mathematical techniques, but recognising the patterns helps you understand what's happening physically.

Curve Watching: Steepening curve = increasing acceleration, flattening curve = decreasing acceleration!

Light Gates in Motion Experiments

Light gates revolutionise motion measurements by eliminating human timing errors. They send a light beam across a gap - when something breaks the beam, precise timing begins or ends.

Unlike stopwatches, light gates don't depend on your reaction time. They respond instantly when objects pass through, giving much more accurate measurements.

Connect them to data loggers and you'll get timing measurements to the nearest millisecond. This precision makes your experimental results far more reliable.

They're particularly brilliant for measuring speeds of moving objects or timing how long objects take to pass through specific points.

Precision Upgrade: Light gates can measure to milliseconds - your reaction time is around 200 milliseconds!