This chapter introduces the fundamental concepts of motion and time. It covers the definition and measurement of speed, the distinction between uniform and non-uniform motion, and the methods used to measure time, including the simple pendulum.
SLOW OR FAST
When evaluating how objects move, it’s clear that some travel more quickly than others, and even a single object can change its pace at different moments.
Key factors in assessing whether an object moves slowly or quickly:
- Vehicle comparison: Watching vehicles heading the same way on a highway allows you to easily spot which one is outpacing the rest.
- Distance traveled over time: Measuring how far objects go within a set period reveals their speed. For example, a bus outdistances a bike over the same duration, showing it’s faster.
- Speed versus time: A quicker vehicle crosses a set distance in fewer moments, reflecting greater speed. In a competition, the winner is the one who finishes the course in the shortest time.
- What speed means: Speed refers to how much ground an object covers in a given time frame. For instance, comparing how far two buses travel in an hour reveals which one is swifter.
- Average speed explained: Often, speed refers to the average, found by dividing the total distance traveled by the total time spent. Take a car covering 50 kilometers in an hour—its average speed is 50 kilometers per hour, even if its pace fluctuated.
- Steady versus uneven motion: An object traveling straight at a consistent rate is in steady motion. If its pace shifts, the motion becomes uneven.
SPEED
Speed shows how rapidly something is moving and can be grasped and quantified in these ways:
- Definition: Speed is the amount of distance an object travels in a set time. By comparing how far multiple objects move in that time, you can tell which is fastest.
- How it’s figured: Speed comes from dividing the total distance traveled by the time it took. The equation is:
Speed = Total distance traveled / Total time spent - Units:
- The standard measure is meters per second (m/s).
- Other options include meters per minute (m/min) or kilometers per hour (km/h).
- Unit symbols stay singular (e.g., 50 km, not 50 kms).
- Understanding average speed: In real-world cases, movement isn’t always steady. So, speed typically means average speed. A car rated at 50 kilometers per hour suggests it’ll cover that distance in an hour, even if it starts slow and speeds up later.
- Steady versus varying motion:
- An object keeping a constant pace on a straight path is in steady motion.
- If its pace alters along that path, it’s in varying motion.
- How it’s measured:
- Speed can be gauged by timing how long it takes to travel a set distance.
- A speedometer, often showing km/h, directly tracks a vehicle’s pace.
- Examples:
- A rocket might hit 8 km/s, while a tortoise creeps at 8 cm/s.
- A chart might list top animal speeds in km/h, like a falcon soaring at 320 km/h.
MEASUREMENT OF TIME
Tracking time involves knowing how it’s measured, the tools involved, and the units used.
Essential elements of time tracking:
- Nature’s cycles: Long ago, people saw that natural events repeat regularly. The gap from one sunrise to the next became a day, a new moon to the next marked a month, and the Earth’s full orbit around the sun defined a year.
- Timekeeping tools: Clocks and watches, relying on repeating actions, are the go-to devices for measuring time.
- Pendulum motion: A simple pendulum swinging back and forth is a classic repeating motion. The time for one full swing is its period, a constant trait Galileo noted, paving the way for pendulum clocks.
- Time units:
- The core unit is the second (s).
- Bigger units include minutes (min) and hours (h).
- Units shift by context—years for age, minutes for a short trip.
- Precision:
- Basic clocks and watches measure down to one second.
- Advanced tools now catch tiny fractions like microseconds (a millionth of a second) or nanoseconds (a billionth).
- Quartz clocks, with electric circuits, outmatch older designs in accuracy.
- Old methods: Before pendulum clocks, sundials, water clocks, and sand timers tracked time across cultures.
- Today’s standards: In India, the National Physical Laboratory in New Delhi keeps time with clocks accurate to a millionth of a second. The world’s top clock, from the U.S.’s National Institute of Standards and Technology, drifts just one second in 20 million years.
Units of Time and Speed
Here’s the breakdown on units for time and speed:
- Time Units:
- The fundamental unit is the second (s).
- Larger ones are minutes (min) and hours (h).
- Speed Units:
- Since speed is distance over time, its base unit is meters per second (m/s).
- Alternatives include meters per minute (m/min) or kilometers per hour (km/h).
- Notes:
- Unit symbols are singular—e.g., 50 km, not 50 kms; 8 cm, not 8 cms.
- Time units vary by purpose, like years for age versus minutes for quick distances.
MEASURING SPEED
Gauging speed means figuring out how fast something moves by tracking its distance over a set period.
Core aspects of speed measurement:
- Speed defined: It’s how much distance an object covers in a unit of time.
- Speed calculation: Use the formula: Speed = Total distance traveled / Total time spent.
- Speed units:
- The primary unit is meters per second (m/s).
- Others include meters per minute (m/min) or kilometers per hour (km/h).
- Tools for tracking speed and distance:
- Speedometer: Found in vehicles like cars and bikes, it shows speed instantly, usually in km/h.
- Odometer: Also in vehicles, it records total distance traveled.
- Hands-on speed check:
- Mark a line, roll a ball along it, and time its start and stop.
- Measure the distance covered to compute speed.
- Ways to find speed:
- Direct approach: Measure distance and time taken.
- Side-by-side: Compare how far objects go in the same time.
- Graphing: Use distance-time graphs to visualize motion and calculate speed.
- A straight line shows steady speed.
- The graph reveals distance at any moment.
- Early techniques: Before modern tools, speed was estimated with sundials, water clocks, or sand timers.
DISTANCE-TIME GRAPH
A distance-time graph uses a line to show an object’s movement, plotting distance against time, offering insights into its motion.
Key features of distance-time graphs:
- Axes:
- The x-axis (horizontal) tracks time; the y-axis (vertical) tracks distance.
- Their meeting point is the origin (O).
- Creating the graph:
- Pick a scale, like 1 min = 1 cm for time and 1 km = 1 cm for distance.
- Mark time and distance values on each axis per the scale.
- Plot points for various time-distance pairs and connect them.
- Reading it:
- A straight line means steady speed (uniform motion).
- A curved or jagged line shows changing speed (non-uniform motion).
- Finding distance and speed:
- Check distance at any time by marking the time on the x-axis, drawing a vertical line to the graph, then a horizontal line to the y-axis for the distance.
- Speed can also be derived from the graph’s slope.
- Choosing a scale:
- Factor in the range of values, midpoints, and paper space.
- Pick a scale that’s easy to plot and read.
NCERT Exercise Question and Answers
- Classification of motion:
- (i) Motion of hands while running: Oscillatory motion.
- (ii) Motion of a horse pulling a cart on a straight road: Motion along a straight line.
- (iii) Motion of a child in a merry-go-round: Circular motion.
- (iv) Motion of a child on a see-saw: Oscillatory motion.
- (v) Motion of the hammer of an electric bell: Oscillatory motion.
- (vi) Motion of a train on a straight bridge: Motion along a straight line.
- Incorrect statements:
- (ii) Every object moves with a constant speed.
- (v) The speed of a train is expressed in m/h.
- Time period of a simple pendulum:
- The pendulum takes 32 seconds to complete 20 oscillations. Therefore, the time period is 32 s / 20 = 1.6 seconds.
- Speed of the train:
- Distance between two stations is 240 km, and the time taken is 4 hours.
- Speed = Distance / Time = 240 km / 4 hours = 60 km/h.
- Distance and speed of the car:
- Initial odometer reading: 57321.0 km at 08:30 AM.
- Final odometer reading: 57336.0 km at 08:50 AM.
- Distance moved = 57336.0 km – 57321.0 km = 15 km.
- Time duration = 08:50 AM – 08:30 AM = 20 minutes.
- Speed in km/min = 15 km / 20 min = 0.75 km/min.
- To express the speed in km/h: 0.75 km/min * 60 min/h = 45 km/h.
- Distance between Salma’s house and school:
- Time taken = 15 minutes = 15 * 60 = 900 seconds.
- Speed = 2 m/s.
- Distance = Speed * Time = 2 m/s * 900 s = 1800 meters.
- Shape of distance-time graph:
- (i) A car moving with a constant speed: A straight line.
- (ii) A car parked on a side road: A straight line parallel to the time axis (x-axis).
- Correct relation:
- (ii) Speed = Distance / Time
- Basic unit of speed:
- (iv) m/s
- Total distance covered by the car:
- First 15 minutes: Speed = 40 km/h, Time = 15/60 = 0.25 hours. Distance = 40 * 0.25 = 10 km.
- Next 15 minutes: Speed = 60 km/h, Time = 15/60 = 0.25 hours. Distance = 60 * 0.25 = 15 km.
- Total distance = 10 km + 15 km = 25 km.
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