9th Class Physics Chapter 2 Kinematics Long Questions

Question 1

How can a vector be represented graphically? Explain.

Accepted Answer

Vectors need direction A vector quantity has both magnitude and direction, so it cannot be shown by a number alone. On paper it is drawn as a straight line with an arrowhead. What the drawing shows The length of the line, on a chosen scale, shows the magnitude.; The arrowhead shows the direction.; The angle of the line, measured from a reference line (x-axis or north), fixes the direction exactly. Steps Choose a suitable scale, for example 1 cm = 100 N.; Draw the reference directions (x-y axes, or north and east).; Work out the length: magnitude ÷ scale.; From the origin, draw a line of that length at the given angle.; Put an arrowhead at the end. Scale: 1 cm = 100 N. Length = 350 ÷ 100 = 3.5 cm. Draw a 3.5 cm line at 60° to the x-axis and add an arrowhead.  In print, a vector is shown in bold (F) or with an arrow over the letter.

Question 2

Differentiate between: (i) rest and motion (ii) speed and velocity.

Accepted Answer

(i) Rest and motion A body does not change its position with respect to its surroundings, A body changes its position with respect to its surroundings; Example: a book lying on a table, Example: a car moving on a road; Relative: a passenger is at rest in a moving bus, Relative: the same passenger is moving with respect to the road Rest and motion are relative: they depend on what the body is compared with. (ii) Speed and velocity Distance covered in unit time, Displacement covered in unit time (rate of change of displacement); Scalar: magnitude only, Vector: magnitude and direction; v = distance ÷ time, v = displacement ÷ time; Never negative, Can be negative (opposite direction); Same on a circular track at a steady pace, Changes on a circular track, because the direction changes; SI unit m s⁻¹, SI unit m s⁻¹

Question 3

Describe the different types of motion, with examples.

Accepted Answer

Introduction Bodies move in different ways. Motion is divided into three types. 1. Translatory motion Translatory motion: Motion in which every particle of the body moves the same distance in the same direction, so the whole body shifts from one place to another. Linear, Straight line, A car on a straight road; a stone falling; Circular, A circle around a point, A stone whirled on a string; a car on a round track; Random, Irregular, no pattern, A flying bee; dust particles in air 2. Rotatory motion Rotatory motion: The body spins about an axis passing through itself. Examples: a ceiling fan, a spinning top, a wheel, the Earth spinning on its axis. 3. Vibratory motion Vibratory motion: The body moves to and fro about a mean position. Examples: a swing, a simple pendulum, the string of a guitar. Circular motion is around a point outside the body; rotatory motion is about an axis through the body.

Question 4

Explain the difference between distance and displacement.

Accepted Answer

Distance Distance: The total length of the path actually travelled, whatever its direction. It is a scalar; SI unit metre. Example: the road from Lahore to Multan is about 320 km long, so a car driving it covers a distance of about 320 km. Displacement Displacement: The shortest straight-line distance from the starting point to the final point, in the direction from start to end. It is a vector; SI unit metre. Differences Scalar, Vector; Depends on the path taken, Depends only on the start and end points; Always positive, Can be zero after a round trip; Always ≥ displacement, Always ≤ distance The runner covers the whole track: distance = 400 m. She ends where she started: displacement = 0.  They are equal only for straight-line motion in one direction.

Question 5

What do the gradients of a distance-time graph and a speed-time graph represent? Explain by drawing diagrams.

Accepted Answer

Gradient (slope) The gradient of a straight line is how steeply it rises: rise ÷ run. To find it, pick two points on the line and draw a right-angled triangle under it. Gradient of a distance-time graph = speed gradient = ΔS ÷ Δt = speed A steeper line means a greater speed. A flat (horizontal) line means the distance is not changing: the body is at rest. A curve getting steeper means the speed is increasing. Gradient of a speed-time graph = acceleration gradient = Δv ÷ Δt = acceleration A rising straight line means uniform acceleration, a falling one uniform deceleration, and a horizontal line zero acceleration (constant speed). A speed-time line rises from 0 to 20 m s⁻¹ in 10 s. Gradient = 20 ÷ 10. acceleration = 2 m s⁻²

Question 6

Prove that the area under a speed-time graph is equal to the distance covered by an object.

Accepted Answer

Idea Distance = speed × time. On a speed-time graph, speed is the height and time is the width, so speed × time is an area. Case 1: constant speed The graph is a horizontal line at height v, so the area under it is a rectangle. Area = length × breadth = t × v. Distance = speed × time = v × t. area = distance Case 2: uniform acceleration from rest The graph is a straight line from 0 to v, so the area under it is a triangle. Area = ½ × base × height = ½ × t × v. Average speed = (0 + v) ÷ 2 = v/2, so distance = (v/2) × t = ½vt. area = distance Conclusion In every case the area between a speed-time graph and the time axis equals the distance covered. For more complicated graphs, split the area into rectangles and triangles and add them.

Question 7

How can the equations of motion be applied to bodies moving under the action of gravity?

Accepted Answer

Free fall Near the Earth, a freely falling body (air resistance ignored) has a uniform acceleration g ≈ 10 m s⁻², the same for every body. So the equations of motion apply, with a replaced by g and S by height h. vf = vᵢ + gt     h = vᵢt + ½gt²     2gh = vf² − vᵢ² Sign rules Body dropped (falling down), vᵢ = 0, +10 m s⁻² (it speeds up); Body thrown up (going up), vf = 0 at the top, −10 m s⁻² (it slows down) Example 1: a body falling h = vᵢt + ½gt² with vᵢ = 0: 80 = ½ × 10 × t². t² = 16. t = 4 s Example 2: a body thrown up At the top vf = 0; g = −10 m s⁻². 2gh = vf² − vᵢ²: 2(−10)h = 0 − 400. h = 20 m The time going up equals the time coming down, and at the top the velocity is zero but the acceleration is still g downward.

Question 8

Define speed, velocity and acceleration. Give their units and explain their types.

Accepted Answer

Speed Speed: Distance covered in unit time: v = S ÷ t. Scalar; SI unit m s⁻¹. Uniform speed: equal distances in equal intervals of time.; Variable speed: unequal distances in equal intervals.; Average speed: total distance ÷ total time. Velocity Velocity: Rate of change of displacement, in a stated direction. Vector; SI unit m s⁻¹. Uniform velocity: equal displacements in equal intervals, in the same direction.; Variable velocity: the speed or the direction (or both) changes.; Average velocity: total displacement ÷ total time. Acceleration Acceleration: Rate of change of velocity: a = (vf − vᵢ) ÷ t. Vector; SI unit m s⁻². Uniform acceleration: velocity changes by equal amounts in equal intervals.; Variable acceleration: the change is not equal in equal intervals.; Deceleration (retardation): velocity decreases; a is negative. vf = 252 ÷ 3.6 = 70 m s⁻¹. a = (70 − 0) ÷ 20. 3.5 m s⁻²

Question 9

Derive the three equations of motion by the graphical method.

Accepted Answer

Set-up A body moves in a straight line with uniform acceleration a. Its velocity is vᵢ at time 0 and vf at time t, and it covers distance S. Its speed-time graph is a straight line from vᵢ up to vf. 1st equation: vf = vᵢ + at Gradient of the speed-time line = acceleration: a = (vf − vᵢ) ÷ t. Multiply both sides by t: at = vf − vᵢ. vf = vᵢ + at 2nd equation: S = vᵢt + ½at² Distance = area under the line = rectangle + triangle. Rectangle = base × height = t × vᵢ. Triangle = ½ × base × height = ½ × t × (vf − vᵢ) = ½ × t × at = ½at². S = vᵢt + ½at² 3rd equation: 2aS = vf² − vᵢ² The whole area is a trapezium: S = ½(vᵢ + vf) × t. From the 1st equation, t = (vf − vᵢ) ÷ a. S = ½(vf + vᵢ)(vf − vᵢ) ÷ a = (vf² − vᵢ²) ÷ 2a. 2aS = vf² − vᵢ² These equations hold only for uniform acceleration in a straight line.

Question 10

Explain distance-time graphs for a body (i) at rest (ii) moving with uniform speed (iii) moving with variable speed. How is speed found from such a graph?

Accepted Answer

What the graph shows Time is on the x-axis and distance on the y-axis. The shape of the line shows how the body moves. (i) Body at rest The distance does not change as time passes, so the graph is a horizontal straight line parallel to the time axis. Its gradient is zero: speed = 0. (ii) Uniform speed Equal distances are covered in equal times, so the graph is a straight line sloping upward. A steeper line means a greater speed. (iii) Variable speed The graph is a curve. If it gets steeper, the speed is increasing; if it gets flatter, the speed is decreasing. Finding the speed speed = gradient = ΔS ÷ Δt ΔS = 80 − 20 = 60 m; Δt = 8 − 2 = 6 s. Speed = 60 ÷ 6. 10 m s⁻¹

Question 11

Explain speed-time graphs for a body moving with (i) constant speed (ii) uniform acceleration (iii) uniform deceleration. How are acceleration and distance found from them?

Accepted Answer

What the graph shows Time is on the x-axis and speed on the y-axis. (i) Constant speed The speed does not change: a horizontal line. Acceleration = 0. (ii) Uniform acceleration The speed rises by equal amounts in equal times: a straight line sloping upward. (iii) Uniform deceleration The speed falls by equal amounts in equal times: a straight line sloping downward. Finding acceleration and distance acceleration = gradient = Δv ÷ Δt distance = area under the graph Acceleration = (30 − 10) ÷ 4 = 5 m s⁻². Distance = area of the trapezium = ½ × (10 + 30) × 4 = 80 m. 5 m s⁻² and 80 m

Question 12

What are scalars and vectors? Explain the head-to-tail rule for adding vectors with an example.

Accepted Answer

Scalars and vectors Scalar: A quantity fully described by its magnitude alone: mass, time, distance, speed, energy. Vector: A quantity that needs magnitude and direction: displacement, velocity, acceleration, force, weight. Resultant vector Resultant vector: The single vector that has the same effect as two or more vectors together. Head-to-tail rule Draw the first vector to scale in its direction.; Draw the second vector to the same scale, its tail starting at the head of the first.; Repeat for any more vectors.; Join the tail of the first to the head of the last: this is the resultant. Measure its length and angle. Draw 3 km west, then 4 km south from its head (scale 1 cm = 1 km). The resultant joins start to end; the two walks are at right angles, so R = √(3² + 4²) = 5 km. displacement = 5 km towards the south-west (the distance walked is 7 km)

Question 13

What is free fall? Describe the motion of a ball thrown vertically upward.

Accepted Answer

Free fall Free fall: The motion of a body under gravity alone, with air resistance neglected. Every freely falling body has the same acceleration g ≈ 10 m s⁻² downward. Going up The ball leaves the hand with velocity vᵢ upward. Gravity acts downward, opposite to the motion, so the ball slows down by 10 m s⁻¹ every second (g = −10 m s⁻²). At the highest point The velocity becomes zero for an instant. The acceleration is still g downward, so the ball does not stay there. Coming down Now gravity acts in the direction of motion, so the ball speeds up by 10 m s⁻¹ every second, and reaches the hand at the speed it was thrown. Time to the top: 0 = 30 − 10t, so t = 3 s. Height: h = vᵢ² ÷ 2g = 900 ÷ 20 = 45 m. Total time in the air = 3 s up + 3 s down = 6 s. 3 s, 45 m, back after 6 s

Rest	Motion
A body does not change its position with respect to its surroundings	A body changes its position with respect to its surroundings
Example: a book lying on a table	Example: a car moving on a road
Relative: a passenger is at rest in a moving bus	Relative: the same passenger is moving with respect to the road

Speed	Velocity
Distance covered in unit time	Displacement covered in unit time (rate of change of displacement)
Scalar: magnitude only	Vector: magnitude and direction
v = distance ÷ time	v = displacement ÷ time
Never negative	Can be negative (opposite direction)
Same on a circular track at a steady pace	Changes on a circular track, because the direction changes
SI unit m s⁻¹	SI unit m s⁻¹

Kind	Path	Examples
Linear	Straight line	A car on a straight road; a stone falling
Circular	A circle around a point	A stone whirled on a string; a car on a round track
Random	Irregular, no pattern	A flying bee; dust particles in air

Distance	Displacement
Scalar	Vector
Depends on the path taken	Depends only on the start and end points
Always positive	Can be zero after a round trip
Always ≥ displacement	Always ≤ distance

Case	Known values	g taken as
Body dropped (falling down)	vᵢ = 0	+10 m s⁻² (it speeds up)
Body thrown up (going up)	vf = 0 at the top	−10 m s⁻² (it slows down)

Long Questions with Answers

Set A: Textbook comprehensive questions 7 questions

How can a vector be represented graphically? Explain.

Vectors need direction

What the drawing shows

Steps

Differentiate between: (i) rest and motion (ii) speed and velocity.

(i) Rest and motion

(ii) Speed and velocity

Describe the different types of motion, with examples.

Introduction

1. Translatory motion

2. Rotatory motion

3. Vibratory motion

Explain the difference between distance and displacement.

Distance

Displacement

Differences

What do the gradients of a distance-time graph and a speed-time graph represent? Explain by drawing diagrams.

Gradient (slope)

Gradient of a distance-time graph = speed

Gradient of a speed-time graph = acceleration

Prove that the area under a speed-time graph is equal to the distance covered by an object.

Idea

Case 1: constant speed

Case 2: uniform acceleration from rest

Conclusion

How can the equations of motion be applied to bodies moving under the action of gravity?

Free fall

Sign rules

Example 1: a body falling

Example 2: a body thrown up

Set B: More important long questions 6 questions

Define speed, velocity and acceleration. Give their units and explain their types.

Speed

Velocity

Acceleration

Derive the three equations of motion by the graphical method.

Set-up

1st equation: vf = vᵢ + at

2nd equation: S = vᵢt + ½at²

3rd equation: 2aS = vf² − vᵢ²

Explain distance-time graphs for a body (i) at rest (ii) moving with uniform speed (iii) moving with variable speed. How is speed found from such a graph?

What the graph shows

(i) Body at rest

(ii) Uniform speed

(iii) Variable speed

Finding the speed

Explain speed-time graphs for a body moving with (i) constant speed (ii) uniform acceleration (iii) uniform deceleration. How are acceleration and distance found from them?

What the graph shows

(i) Constant speed

(ii) Uniform acceleration

(iii) Uniform deceleration

Finding acceleration and distance

What are scalars and vectors? Explain the head-to-tail rule for adding vectors with an example.

Scalars and vectors

Resultant vector

Head-to-tail rule

What is free fall? Describe the motion of a ball thrown vertically upward.

Free fall

Going up

At the highest point

Coming down

The rest of Chapter 2

Long Questions from other Physics chapters