Q1: A car travels 100 km north, then 60 km south. What is the magnitude of its displacement? (a) 160 km (b) 100 km (c) 60 km (d) 40 km
Solution:
Ans: (d) Explanation: Displacement is the shortest distance from initial to final position. Net displacement = 100 km - 60 km = 40 km in the north direction.
Q2: Which of the following is a scalar quantity? (a) Displacement (b) Velocity (c) Distance (d) Acceleration
Solution:
Ans: (c) Explanation: Distance requires only magnitude for its explanation and has no direction, making it a scalar quantity unlike displacement, velocity, and acceleration.
Q3: A body moving in a circular path completes one revolution. What is its displacement? (a) Equal to the circumference (b) Zero (c) Equal to the diameter (d) Equal to the radius
Solution:
Ans: (b) Explanation: After one complete revolution, the object returns to its original position. Since initial and final positions are the same, displacement equals zero.
Q4: What does the slope of a position-time graph represent? (a) Distance (b) Velocity (c) Acceleration (d) Displacement
Solution:
Ans: (b) Explanation: The slope of the position-time graph gives the average velocity of the object, calculated as change in position divided by time interval.
Q5: In uniform circular motion, which quantity remains constant? (a) Velocity (b) Acceleration (c) Speed (d) Direction of motion
Solution:
Ans: (c) Explanation: In uniform circular motion, the speed remains constant at every point, but the direction of velocity changes continuously along the tangent to the circle.
Fill in the Blanks
Q1: Physical quantities which require specifying both the direction and magnitude are called _____.
Solution:
Ans: vectors
Q2: The SI unit of average acceleration is _____.
Solution:
Ans: m s⁻²
Q3: If an object travels equal distances in equal intervals of time, it is said to be in _____ motion.
Solution:
Ans: uniform
Q4: The area enclosed between velocity-time graph and time axis gives the _____.
Solution:
Ans: displacement
Q5: For one complete revolution in circular motion, the distance travelled equals _____.
Solution:
Ans: 2πR
True or False
Q1: Distance is always greater than or equal to the magnitude of displacement.
Solution:
Ans: True Explanation: Distance is the total path length covered while displacement is the shortest path, so distance is always greater than or equal to displacement.
Q2: An object moving at constant velocity on a highway has zero acceleration.
Solution:
Ans: True Explanation: Acceleration depends on how quickly velocity changes. If velocity is constant, there is no change, resulting in zero acceleration despite fast motion.
Q3: Average speed and average velocity are always equal for motion in a straight line.
Solution:
Ans: False Explanation: Average speed equals magnitude of average velocity only when motion is in one direction without turning back; otherwise they can differ significantly.
Q4: The slope of a velocity-time graph gives the acceleration of the object.
Solution:
Ans: True Explanation: Acceleration is calculated as change in velocity divided by time interval, which is exactly what the slope of velocity-time graph represents.
Q5: In uniform circular motion, the object is not accelerated because speed is constant.
Solution:
Ans: False Explanation: Even though speed is constant, the direction of velocity changes continuously in circular motion, causing acceleration due to change in direction alone.
Match the Following
Column A
Column B
1. Distance
A. Change in velocity divided by time
2. Displacement
B. Metre per second
3. Average velocity
C. Actual path length travelled
4. Average acceleration
D. Motion with constant speed in circular path
5. Uniform circular motion
E. Shortest distance from initial to final position
Solution:
Ans:
1 - C: Distance is defined as the actual path length travelled by an object from its initial to final position.
2 - E: Displacement is the shortest distance travelled by an object from its initial position to its final position with direction.
3 - B: The SI unit of average velocity is metre per second, same as speed, as it measures rate of change of position.
4 - A: Average acceleration is defined as the change in velocity of an object divided by the corresponding time interval taken.
5 - D: Uniform circular motion occurs when an object moves in a circular path with constant speed but changing direction of velocity.
Short Answer Questions
Q1: Explain the difference between distance and displacement with an example.
Solution:
Ans: Distance is the actual path length travelled and is a scalar quantity requiring only magnitude. Displacement is the shortest distance from initial to final position and is a vector quantity requiring both magnitude and direction. For example, if a person walks 4 km north then 4 km east, the total distance is 8 km, but the displacement is approximately 5.66 km northeast.
Q2: Why does uniform circular motion have acceleration even though speed is constant?
Solution:
Ans: In uniform circular motion, the speed remains constant but the direction of velocity changes continuously at every point along the circular path. Since velocity is a vector quantity that depends on both magnitude and direction, any change in direction results in a change in velocity. Acceleration is defined as the rate of change of velocity, so even with constant speed, the changing direction causes acceleration.
Q3: What information can be obtained from the slope and area of a velocity-time graph?
Solution:
Ans: The slope of a velocity-time graph represents the acceleration of the object, calculated as change in velocity divided by time interval. A positive slope indicates acceleration in the direction of velocity, while a negative slope indicates deceleration. The area enclosed between the velocity-time graph and the time axis represents the displacement of the object during that time interval, calculated using appropriate geometric shapes.
Q4: Define average velocity and explain how it differs from average speed.
Solution:
Ans: Average velocity is defined as the displacement divided by the time interval taken. It is a vector quantity requiring both magnitude and direction. Average speed is the total distance travelled divided by time interval and is a scalar quantity with only magnitude. For motion in a straight line in one direction, they are equal, but if motion involves turning back, average velocity can be zero while average speed is non-zero.
Q5: What is meant by constant acceleration? Give an example.
Solution:
Ans: Constant acceleration occurs when an object moving in a straight line in the same direction experiences equal changes in the magnitude of its velocity during equal intervals of time. This means the rate of change of velocity remains uniform throughout the motion. An example is a car starting from rest and increasing its speed by 5 m/s every second, maintaining a constant acceleration of 5 m/s² throughout.
Long Answer Questions
Q1: Derive the first equation of motion (v = u + at) using the graphical method and explain its significance.
Solution:
Ans: Consider a velocity-time graph where initial velocity is u at point A (time t = 0) and final velocity is v at point B (time = t). The acceleration is the slope of the line AB. Using the definition of acceleration: a = (change in velocity)/(change in time) = (v - u)/(t - 0). Rearranging gives v - u = at, therefore v = u + at. This equation relates final velocity to initial velocity, acceleration, and time, allowing prediction of velocity at any instant for uniformly accelerated motion.
Q2: Explain why maintaining safe distance between vehicles is important and what factors affect stopping distance.
Solution:
Ans: When brakes are applied, vehicles don't stop immediately but travel a certain stopping distance. This distance depends on several factors:
Velocity: Higher speeds result in longer stopping distances
Road surface condition: Wet or icy roads increase stopping distance compared to dry roads
Braking capacity: The negative acceleration achievable by brakes varies between vehicles
Driver's reaction time: Time taken to respond and apply brakes affects total stopping distance
Safe distance must be adjusted based on initial velocity to prevent collisions and ensure road safety.
Q3: Compare uniform motion and non-uniform motion. Analyze how their position-time and velocity-time graphs differ.
Solution:
Ans: In uniform motion, an object travels equal distances in equal time intervals with constant velocity. Its position-time graph is a straight line with constant slope, and velocity-time graph is a horizontal line parallel to the time axis showing zero acceleration. In non-uniform motion, the object travels unequal distances in equal time intervals with changing velocity. Its position-time graph is a curve with varying slope, and velocity-time graph is a sloping line indicating constant acceleration or a curve for variable acceleration.
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