Chapter 8: Measurement of Time and Motion

Motion: An object is said to be in motion when its position changes with respect to a reference point (observer) over time. Motion is always relative — the same object can be in motion relative to one observer and at rest relative to another.

Speed: The distance covered by an object per unit time. Formula: Speed = Distance ÷ Time (S = D/T)

• Average speed = Total distance ÷ Total time
• Unit: m/s (SI), km/h (practical)
• Conversion: 1 km/h = 1000/3600 m/s = 5/18 m/s; 1 m/s = 18/5 km/h = 3.6 km/h

Uniform Motion: Equal distances covered in equal time intervals. Distance–time graph is a straight line through the origin. Slope of the graph = speed.

Non-Uniform Motion: Unequal distances covered in equal time intervals. Distance–time graph is a curve. The speed is changing (accelerating or decelerating).

Periodic Motion: Motion that repeats after a fixed time interval (time period). Examples: pendulum of a clock, Earth's rotation (24 hours), Earth's revolution (365.25 days), heartbeat (~72 beats per minute), vibrating guitar string.

Pendulum: A mass (bob) suspended from a fixed point that swings back and forth. Time period of a pendulum depends only on its length (T = 2π√(L/g)) — not on the mass or amplitude (for small angles). A longer pendulum has a longer time period.

SI Units of Time:

• 1 minute = 60 seconds
• 1 hour = 3600 seconds
• 1 day = 86,400 seconds
• 1 year = 365.25 days = 31,557,600 seconds
• Smaller units: millisecond (10⁻³ s), microsecond (10⁻⁶ s), nanosecond (10⁻⁹ s) — relevant for electronics and computing

Distance–Time Graphs — Reading and Interpretation

Distance–time graphs are a core CSAT and conceptual physics topic:

1. Straight line with positive slope: Uniform motion; slope = speed
2. Horizontal line (zero slope): Object is at rest (not moving)
3. Curve (slope increasing): Object is accelerating (getting faster)
4. Curve (slope decreasing): Object is decelerating (slowing down)
5. Two segments with different slopes: Object moved at different speeds at different times

Speed–time graphs (different from distance–time):

• Area under speed–time graph = distance travelled
• Slope of speed–time graph = acceleration

CSAT Speed-Distance-Time Problems: Formula triangle: Speed = Distance/Time; Distance = Speed × Time; Time = Distance/Speed Common trap: Mixing units (km with hours but m with seconds). Always check units.

Measurement in History — India's Contribution:

• The Indian Standard Time (IST) is UTC + 5:30. Set by meridian passing through Mirzapur, UP (82.5°E longitude).
• India does not follow Daylight Saving Time (unlike many countries).
• ISRO's Master Control Facility (MCF) at Hassan (Karnataka) and Bhopal controls synchronisation of satellite clocks.
• Jantar Mantar observatories (Jaipur, Delhi, Mathura, Varanasi, Ujjain) built by Maharaja Jai Singh II (18th century) for precise astronomical time measurement — UNESCO World Heritage Site (Jaipur Jantar Mantar).