Get step-by-step solutions for Chapter 2 “Kinematics” from the 9th class physics new syllabus. Specifically designed for Lahore Board and all Punjab Boards, this guide helps students excel in their exams.
MCQs
2.1 The numerical ratio of displacement to distance is:
Options:
(a) always less than one
(b) always equal to one
(c) always greater than one
(d) equal to or less than one
Answer: (d) equal to or less than one
Explanation: Displacement is the shortest distance between two points and can be equal to or less than the actual distance traveled. It cannot exceed the distance.
2.2 If a body does not change its position with respect to some fixed point, then it will be in a state of:
Options:
(a) rest
(b) motion
(c) uniform motion
(d) variable motion
Answer: (a) rest
Explanation: A body is said to be at rest when it does not change its position relative to a reference point.
Tip: Relate to the definition of rest and motion.
2.3 A ball is dropped from the top of a tower; the distance covered by it in the first second is:
Options:
(a) 5 m
(b) 10 m
(c) 50 m
(d) 100 m
Answer: (a) 5 m
Explanation: The distance covered in free fall is given by s=1/2gt2
s=1/2×10×(1)2=5 m
Tip: Memorize the formula s=1/2gt2
2.4 A body accelerates from rest to a velocity of 144 km/h in 20 seconds. Then the distance covered by it is:
Options:
(a) 100 m
(b) 400 m
(c) 1400 m
(d) 1440 m
Answer: (c) 1400 m
Explanation: Convert 144 km/h
v=144×1000/3600=40 m/s
Using the formula s=1/2at2
First, calculate acceleration: a=vt=40/20=2 m/s2
Then, s=1/2×2×202=1400 m
Tip: Convert units before calculations.
2.5 A body is moving with constant acceleration starting from rest. It covers a distance S in 4 seconds. How much time does it take to cover one-fourth of this distance?
Options:
(a) 1 s
(b) 2 s
(c) 4 s
(d) 16 s
Answer: (b) 2 s
Explanation: For constant acceleration, distance is proportional to the square of time:
S∝t2
If the total time is t=4 s, one-fourth of the distance is covered in t/2=2
Tip: Remember the proportionality S∝t2
2.6 The displacement-time graphs of two objects A and B are shown in the figure. Point out the true statement from the following:
Options:
(a) The velocity of A is greater than B.
(b) The velocity of A is less than B.
(c) The velocity of A is equal to that of B.
(d) The graph gives no information in this regard.
Answer: (a) The velocity of A is greater than B.
Explanation: The slope of a displacement-time graph represents velocity. Since the slope of A’s graph is steeper than B’s, A has a greater velocity.
Tip: Compare slopes for velocity on such graphs.
2.7 The area under the speed-time graph is numerically equal to:
Options:
(a) velocity
(b) uniform velocity
(c) acceleration
(d) distance covered
Answer: (d) distance covered
Explanation: The area under a speed-time graph represents the distance traveled by the object.
Tip: Always associate “area under the curve” with specific physical quantities based on the graph type.
2.8 Gradient of the speed-time graph is equal to:
Options:
(a) speed
(b) velocity
(c) acceleration
(d) distance covered
Answer: (c) acceleration
Explanation: The gradient (slope) of a speed-time graph gives the rate of change of speed, which is acceleration.
Tip: For speed-time graphs:
- Slope → Acceleration
- Area under the curve → Distance.
2.9 Gradient of the distance-time graph is equal to:
Options:
(a) speed
(b) velocity
(c) distance covered
(d) acceleration
Answer: (b) velocity
Explanation: The gradient of a distance-time graph represents the rate of change of distance with time, which is velocity.
Tip: Remember, distance-time graph slope indicates motion speed or velocity.
2.10 A car accelerates uniformly from 80.5 km/h at t=0 to 113 km/h at t=9 s. Which graph best describes the motion of the car?
Answer: (a)
Explanation: For uniform acceleration, the velocity-time graph is a straight line with a positive slope, as shown in option (a).
Tip: Uniform acceleration always produces a straight, inclined line in velocity-time graphs.
B: Short Answer Questions
2.1 Define scalar and vector quantities.
Answer:
- Scalar quantities: Physical quantities that have magnitude only (e.g., mass, temperature).
- Vector quantities: Physical quantities that have both magnitude and direction (e.g., force, velocity).
2.2 Give 5 examples each for scalar and vector quantities.
Answer:
- Scalars: Speed, mass, temperature, time, energy.
- Vectors: Velocity, force, acceleration, displacement, momentum.
2.3 State head-to-tail rule for addition of vectors.
Answer: Place the tail of the second vector at the head of the first vector. The resultant vector is drawn from the tail of the first vector to the head of the second vector.
2.4 What are distance-time graph and speed-time graph?
Answer:
- Distance-time graph: Represents the motion of an object by plotting distance against time. Slope indicates speed.
- Speed-time graph: Represents the variation of speed with time. Slope gives acceleration, and the area under the curve gives distance.
2.5 Falling objects near the Earth have the same constant acceleration. Does this imply that a heavier object will fall faster than a lighter object?
Answer: No, all objects fall with the same acceleration (9.8 m/s²) near the Earth, regardless of mass, due to gravity (neglecting air resistance).
2.6 The vector quantities are sometimes written in scalar notation (not bold face). How is the direction indicated?
Answer: Direction is indicated using angles, signs (+/-), or directional symbols (e.g., North, South, East, West).
2.7 A body is moving with uniform speed. Will its velocity be uniform? Give reason.
Answer: Not necessarily. If the body changes direction, the velocity will not remain uniform even if the speed is constant because velocity is a vector quantity (depends on both magnitude and direction).
2.8 Is it possible for a body to have acceleration when moving with:
(i) Constant velocity?
Answer: No, because acceleration is the rate of change of velocity, and with constant velocity, there is no change.
(ii) Constant speed?
Answer: Yes, if the direction changes (e.g., circular motion), there can be centripetal acceleration.
C: Constructed Response Questions
2.1 Distance and displacement may or may not be equal in magnitude. Explain this statement.
Answer:
- Equal: When the motion is in a straight line without changing direction. For example, walking 5 meters straight.
- Not Equal: When the motion involves a change in direction, displacement (shortest path) will be less than the distance (total path). For example, walking in a circular path.
2.2 When a bullet is fired, its velocity with which it leaves the barrel is called the muzzle velocity of the gun. The muzzle velocity of one gun with a longer barrel is less than that of another gun with a shorter barrel. In which gun is the acceleration of the bullet larger? Explain your answer.
Answer:
The gun with the shorter barrel has larger acceleration because the same change in velocity (muzzle velocity) occurs over a shorter distance, leading to greater acceleration (since a=v2−u2/2s, where ss is the distance).
2.3 For a car moving at uniform speed, the area under the speed-time graph is calculated. Its value came out to be positive. Is it possible that its instantaneous velocity at any time during the trip had the negative sign? Give justification of your answer.
Answer:
No, because the speed-time graph shows the magnitude of velocity, which is always positive. If the graph is used to compute displacement (not speed), the instantaneous velocity could be negative if the car changes direction.
Comprehensive questions
2.1 How can a vector be represented graphically? Explain.
- A vector is represented graphically as a directed line segment.
- The length of the line represents the magnitude of the vector, and the arrowhead shows its direction.
- For example, if a vector shows a displacement of 5 meters to the right, draw a 5 cm arrow pointing to the right (scale: 1 cm = 1 m).
2.2 Differentiate between:
(i) Rest and Motion:
- Rest: An object is at rest when it does not change its position relative to a reference point.
Example: A book lying on a table is at rest.
- Motion: An object is in motion when it changes its position relative to a reference point.
Example: A car moving on a road is in motion.
(ii) Speed and Velocity:
- Speed: It is the rate of change of distance and has no direction (scalar quantity).
Example: A car moving at 60 km/h.
- Velocity: It is the rate of change of displacement and includes direction (vector quantity).
Example: A car moving 60 km/h east.
2.3 Describe different types of motion. Also give examples.
- Translational Motion: Movement in a straight or curved path.
Example: A car driving on a straight road or a ball rolling downhill.
- Rotational Motion: Movement around a fixed axis.
Example: The spinning of a fan.
- Oscillatory Motion: Repeated to-and-fro motion.
Example: The swinging of a pendulum.
- Random Motion: Unpredictable movement in any direction.
Example: The movement of dust particles in the air.
2.4 Explain the difference between distance and displacement.
- Distance:
- The total path covered by an object.
- It is a scalar quantity (only magnitude).
- Example: If a person walks 4 m north and then 3 m south, the distance is 4+3=7 m
- Displacement:
- The shortest straight-line distance between the initial and final position of an object.
- It is a vector quantity (magnitude and direction).
- Example: For the same movement above, displacement = 4−3=1 m north.
2.5 What do gradients of distance-time graph and speed-time graph represent? Explain it by drawing diagrams.
- Distance-Time Graph:
- The gradient (slope) represents the speed. A steeper slope means higher speed.
- Example: A straight, slanted line shows uniform speed, while a curved line shows acceleration or deceleration.
- Speed-Time Graph:
- The gradient represents acceleration. A straight, inclined line shows uniform acceleration.
- Example: If the slope is zero (horizontal line), the speed is constant.
2.6 Prove that the area under speed-time graph is equal to the distance covered by an object.
- The area under a speed-time graph represents the product of speed and time, which gives distance.
- Proof:
- Speed = Distance ÷ Time → Distance = Speed × Time
- For a speed-time graph, the area of a rectangle (or triangle for acceleration) gives the distance:
- Area = Base × Height = Time × Speed = Distance.
- Example: For a car moving at 10 m/s for 5 seconds, the graph’s area = 10×5=50 m
2.7 How equations of motion can be applied to bodies moving under the action of gravity?
- Equations of motion are:
- v=u+at
- s=ut+1/2at2
- v2=u2+2as
- For objects in free fall:
- Initial velocity u=0u = 0 (if dropped).
- Acceleration a=g=9.8 m/s2 (gravity).
- Example: If a ball is dropped from a height of 20 m:
- Use s=1/2gt2
20=1/2(9.8)t2 → t=2.02 s
The equations help determine time, velocity, or height for objects under gravity.
