Introduction to Linear Motion
Definition: Linear motion is a type of movement where an object travels in a straight line from one place to another. This means the object doesn’t turn, curve, or move in circles—it just goes straight forward or backward. An example is a car moving along a straight road or a ball rolling straight across the floor.
Describing quantities: When we study linear motion, we use five important measurements to describe it: distance (how far something moves), displacement (how far and in which direction), speed (how fast), velocity (how fast and in what direction), and acceleration (how quickly speed or direction changes). These help us understand how the object is moving and how its motion changes over time.
Types of Linear Motion
Uniform velocity: This happens when something moves at the same speed in a straight line without changing its direction or speed. In this case, there is no speeding up or slowing down—so, acceleration is zero. For example, a toy car moving steadily along a straight track at 2 m/s is in uniform motion.
Non-uniform motion: This type of motion occurs when an object changes its speed or direction while moving. This means the object is accelerating or decelerating, so its velocity is not constant. A car speeding up, slowing down, or turning while driving would be showing non-uniform motion.
Stationary: When something is stationary, it means it is not moving at all. It stays in one place without going forward, backward, or in any direction. For example, a book lying on a table is stationary because it doesn’t change position.
Key Concepts
Distance: Distance tells us the total length of the path an object has travelled, no matter which direction it went. It’s a scalar quantity, which means it only has size (how much), not direction. We measure distance in metres (m). For example, if you walk around a park and end up where you started, your distance might be 500 m even if your final position hasn’t changed.
Displacement: Displacement is the straight-line distance from where something started to where it ended, including the direction. It is a vector quantity, which means it includes both size and direction. It is also measured in metres (m). For example, if you walk 3 m forward and then 3 m back to your starting point, your displacement is 0 m, because you ended up where you began.
Speed: Speed tells us how fast something is moving. It is found by dividing the total distance travelled by the total time taken. Speed is a scalar quantity and is measured in metres per second (m/s). For instance, if a car travels 100 m in 10 seconds, its speed is 10 m/s.
Velocity: Velocity is similar to speed, but it also tells us the direction of motion. It is the rate at which displacement changes. Velocity is a vector and also measured in m/s. So, if a car moves east at 20 m/s, that direction matters and makes it velocity, not just speed.
Acceleration: Acceleration is how quickly velocity changes. It can happen when something speeds up, slows down, or changes direction. It is a vector quantity and is measured in metres per second squared (m/s²). A bicycle going faster and faster shows acceleration.
Average acceleration formula: We calculate average acceleration using the formula: a = (v – u) / t, where:
- v is the final velocity (how fast at the end),
- u is the initial velocity (how fast at the start), and
- t is the time taken for the change. This tells us how much the velocity changes each second.
Deceleration: Deceleration is the opposite of acceleration. It means the object is slowing down instead of speeding up. It is shown as a negative acceleration because the velocity is getting smaller over time.
Ticker Tape Timer
Function: A ticker tape timer is a device used in physics experiments to measure motion over very short periods of time. It works by stamping dots on a long strip of paper while the paper is pulled through a vibrating marker. These dots show how an object moves.
Frequency: Most ticker timers work at a frequency of 50 Hz, which means the marker makes 50 dots every second. That also means one dot is made every 0.02 seconds. This helps us know the exact time between each dot.
Measurement: By looking at the distance between the dots, we can figure out how fast or slow something is moving. Closer dots mean slower movement, while further apart dots mean faster movement. You can also use the dots to work out acceleration and how motion changes over time.
Dot patterns:
- Even spacing: If the dots are evenly spaced, the object moved with uniform velocity (same speed).
- Increasing spacing: If the spaces between dots get larger, the object was accelerating (speeding up).
- Decreasing spacing: If the spaces get smaller, the object was decelerating (slowing down).
Equations of Linear Motion (for constant acceleration)
First equation: v = u + at
This equation tells us the final velocity (v) of an object when we know its starting velocity (u), how much it accelerated (a), and how long it moved (t).
Second equation: s = ut + ½ at²
This equation helps us find the distance (s) travelled when an object moves with constant acceleration. It combines the starting speed, time, and how much the object speeds up.
Third equation: s = ½ (u + v)t
This one gives the distance travelled when we know the starting and ending velocities and the time taken. It works like finding the average speed and multiplying it by time.
Fourth equation: v² = u² + 2as
This equation is useful when we don’t know the time. It connects velocity, acceleration, and displacement.
Graphs of Linear Motion
Graph types: In physics, we use three types of graphs to describe linear motion:
- Displacement-time graphs
- Velocity-time graphs
- Acceleration-time graphs Each type of graph shows different information about how an object moves.
Displacement-time gradient: The slope or gradient of a displacement-time graph shows the object’s velocity. A steep line means fast movement, and a flat line means slow movement.
Straight line (displacement-time): A straight line means the object is moving with constant velocity. It is not speeding up or slowing down.
Curved line (displacement-time): A curved line means the object is moving with non-uniform velocity, meaning it’s accelerating or decelerating.
Velocity-time gradient: The slope of a velocity-time graph shows the acceleration. A steep slope means fast acceleration.
Horizontal line (velocity-time): A flat line means the object is moving at a constant velocity. It is not accelerating.
Area under velocity-time graph: If you calculate the area under the line on a velocity-time graph, you get the displacement—how far the object has travelled.
Acceleration-time gradient: This gradient shows how acceleration is changing over time. If the graph is sloping, acceleration is increasing or decreasing.
Horizontal line (acceleration-time): A flat line means the object has constant acceleration—its velocity is changing at the same rate.
Area under acceleration-time graph: This area tells you how much the object’s velocity has changed during the time shown.