Questions & Answers: "Measurement of Time and Motion"

The time period of a simple pendulum is primarily determined by its effective length. A longer string results in a longer time period for one complete oscillation. Factors like the mass of the bob and the amplitude of oscillation (for small angles) do not significantly affect the time period. The material of the string also has no direct influence on how quickly the pendulum swings, as long as it's massless or its mass is negligible compared to the bob.

To find the speed in m/s, first calculate the speed in km/h. Speed is defined as distance divided by time. Given Distance = 162 km, Time = 3 hours. So, Speed = $162 \text{ km} / 3 \text{ hours} = 54 \text{ km/h}$. Next, convert km/h to m/s. We know that $1 \text{ km} = 1000 \text{ m}$ and $1 \text{ hour} = 3600 \text{ s}$. So, $1 \text{ km/h} = (1000 \text{ m}) / (3600 \text{ s}) = 5/18 \text{ m/s}$. Therefore, $54 \text{ km/h} = 54 \times (5/18) \text{ m/s} = 3 \times 5 \text{ m/s} = 15 \text{ m/s}$. Options B, C, and D are incorrect as they result from incorrect unit conversions or calculations.

Oscillatory motion is characterized by an object moving repeatedly back and forth about a central, or mean, position. A child on a swing perfectly demonstrates this to-and-fro motion. A car on a straight road exhibits rectilinear motion, the hands of a clock show circular motion, and a spinning top displays rotational motion.

A distance-time graph for an object moving with uniform speed is represented by a straight line inclined to the time axis. This is because uniform speed implies that the object covers equal distances in equal intervals of time. When distance is plotted against time, this constant rate of change results in a linear relationship. Option A, a straight line parallel to the time axis, indicates that the distance is not changing with time, meaning the object is stationary. Option B, a straight line parallel to the distance axis, is not physically possible as time always progresses. Option D, a curved line, would represent non-uniform speed, where the object's speed is changing (it is either accelerating or decelerating).

The International System of Units (SI) establishes fundamental units for various physical quantities. For distance, the SI unit is the meter (m), and for time, it is the second (s). Since speed is defined as distance traveled per unit time, its standard SI unit is derived by combining these fundamental units, resulting in meters per second (m/s). Other options like km/h, m/min, and cm/s are valid units of speed but are not the designated SI unit.

The time period of a simple pendulum is the time taken to complete one oscillation. It is calculated by dividing the total time taken by the number of oscillations. Here, Time Period = Total Time / Number of Oscillations = 40 seconds / 20 = 2 seconds. Option B is incorrect as it's the reciprocal. Options C and D are simply the number of oscillations and total time, respectively, not the time period.

Uniform motion occurs when an object covers equal distances in equal intervals of time. In this scenario, the car covers equal distances (10 km) but in unequal time intervals (15 minutes, 20 minutes, 25 minutes). Therefore, the car is exhibiting non-uniform motion. Oscillatory motion involves a to-and-fro movement, and periodic motion repeats itself after regular intervals, neither of which describes this situation.

The relationship between speed, distance, and time is given by the formula: Distance = Speed × Time. Given the average speed of the bus is 60 km/h and the time of travel is 2.5 hours. Plugging these values into the formula, the distance covered = 60 km/h × 2.5 hours = 150 km. Option A (120 km) would be the distance for 2 hours. Options C and D are results of incorrect calculations.

On a distance-time graph, a horizontal line parallel to the time axis signifies that the object's distance from its starting point remains constant as time progresses. This indicates that the object is not moving, i.e., it is at rest. Uniform speed would be represented by a straight line with a positive slope. Acceleration or non-uniform speed would be indicated by a curved line or a line with a changing slope, respectively.

The basic unit of time in the International System of Units (SI) is the second (s). While hours are commonly used for convenience, the second is the fundamental unit for scientific measurements.

A simple pendulum exhibits periodic motion because it repeats its motion (swings back and forth) after a fixed interval of time, completing each oscillation in a consistent duration.

Speed is indeed the measure of how fast an object is moving. It is calculated by dividing the total distance traveled by the total time taken, which directly translates to distance covered per unit time ($ext{Speed} = rac{ ext{Distance}}{ ext{Time}}$).

If an object covers unequal distances in equal intervals of time, its motion is defined as non-uniform motion. Uniform motion occurs when an object covers equal distances in equal intervals of time.

The time period of a simple pendulum primarily depends on its length and the acceleration due to gravity. For small displacements, it does not depend on the mass of the bob or the amplitude of its oscillation.

Definition of oscillatory motion, characteristic of motion, and a relevant daily life example.

Clear definition of uniform motion, clear definition of non-uniform motion, and appropriate examples for both.

Basic principle of sundial, components (dial, gnomon), and how time is read.

Correct calculation of speed for both parts, correct identification of motion type, and a clear justification based on the definition of uniform/non-uniform motion.

Definition of simple pendulum, correct identification of factors affecting time period, and correct identification of factors not affecting time period, with brief explanations.

Points will be awarded for:

1. Correct definition of speed.
2. Correct formula for speed.
3. Correct SI unit of speed.
4. Relevant real-life example.
5. Clear description of steps/calculation in the example.