Motion
Kinematics, Graphs & Equations of Motion
In-Text Questions (Page 100)
Q1. An object has moved through a distance. Can it have zero displacement?
Yes, an object can have zero displacement even if it has moved through a distance. This happens when the final position of the object coincides with its initial position (e.g., completing a full circle).
Q2. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement at the end of 2 minutes 20 seconds?
Given: Side = 10 m, Perimeter = 40 m, Time for 1 round = 40 s.
Total Time: 2 min 20 s = 140 s.
Rounds: 140/40 = 3.5 rounds.
In 3.5 rounds, the farmer will be at the diagonally opposite
corner.
Displacement = Diagonal = √(102 + 102) = √200 =
14.14 m.
In-Text Questions (Page 102)
Q1. Distinguish between Speed and Velocity.
| Speed | Velocity |
|---|---|
| Distance travelled per unit time. | Displacement per unit time. |
| Scalar Quantity (Magnitude only). | Vector Quantity (Magnitude + Direction). |
| Always positive. | Can be positive, negative, or zero. |
Q2. Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?
When an object moves in a straight line in a specific direction without turning back, the magnitude of displacement is equal to the distance covered. In this case, average velocity = average speed.
In-Text Questions (Page 103)
Q1. When will you say a body is in (i) uniform acceleration? (ii) non-uniform acceleration?
(i) Uniform Acceleration: If an object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time (e.g., Free fall).
(ii) Non-uniform Acceleration: If the velocity changes at a non-uniform rate (e.g., A car driving in traffic).
Q2. A bus decreases its speed from 80 km/h to 60 km/h in 5 s. Find the acceleration.
Given: u = 80 km/h = 22.22 m/s, v = 60 km/h = 16.66 m/s, t = 5 s.
Step 1: a = (v - u) / t
Step
2: a = (16.66 - 22.22) / 5 = -5.56 / 5
Answer: a = -1.112
m/s2 (Retardation).
In-Text Questions (Page 109)
Q1. A bus starting from rest moves with a uniform acceleration of 0.1 m/s² for 2 minutes. Find (a) the speed acquired, (b) the distance travelled.
Given: u = 0, a = 0.1 m/s2, t = 2 min = 120 s.
(a) Speed (v): v = u + at = 0 + 0.1 × 120 = 12 m/s.
(b) Distance (s): s = ut + ½at² = 0 + 0.5 × 0.1 × (120)² = 0.05 × 14400 = 720 m.
Main Textbook Exercises
Q4. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?
Given: u = 0, a = 3 m/s², t = 8 s.
Formula: s = ut + ½at²
s = 0 + 0.5 × 3 × (8)²
= 1.5 × 64 = 96 m.
Q7. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m/s², with what velocity will it strike the ground? After what time will it strike the ground?
Given: u = 0, s = 20 m, a = 10 m/s².
(i) Final Velocity (v): v² = u² + 2as
v² = 0 + 2 × 10 × 20 = 400
v = √400 = 20 m/s.
(ii) Time (t): v = u + at
20 = 0 + 10t
t
= 20/10 = 2 s.
Motion
In-depth: Graphs & Equations
1. Graphical Representation of Motion
- Uniform Speed: Straight line passing through the origin. Slope gives speed.
- Non-uniform Speed: Curved line.
- Stationary Object: Straight line parallel to the time axis.
- Uniform Motion: Straight line parallel to the time axis. Area under the curve gives displacement.
- Uniform Acceleration: Straight line with positive slope. Slope gives acceleration.
- Uniform Retardation: Straight line with negative slope.
2. Equations of Motion
For numericals involving uniform acceleration, use these three equations:
Velocity-Time Relation
Position-Time Relation
Position-Velocity Relation
Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance/displacement.
3. Uniform Circular Motion
When an object moves in a circular path with uniform speed, its motion is called uniform circular motion.
Velocity is NOT constant: Because the direction of motion keeps changing continuously at every point. Hence, it is accelerated motion.
v = (2πr) / t
Where r = radius of the circular path, t = time taken for one round.
4. Sample Problem
Problem: A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 10 minutes. Find its acceleration.
Given: u = 0 (rest), v = 40 km/h = 40 × 5/18 = 11.11 m/s, t = 10 min = 600 s.
Formula: a = (v - u) / t
Solution: a = (11.11 - 0) / 600 = 0.0185 m/s².
Key Facts & Definitions
50+ Important Points to Remember
Physical quantity having only magnitude (e.g., Distance, Speed).
Physical quantity having both magnitude and direction (e.g., Displacement, Velocity).
Actual path length covered by an object.
Shortest distance between initial and final position.
Possible even if distance is not zero (e.g., returning to start).
Rate of change of distance (Distance/Time).
Rate of change of displacement (Speed with direction).
Object covers equal distances in equal intervals of time.
Object covers unequal distances in equal intervals of time.
Rate of change of velocity ((v-u)/t).
meter per second (m/s).
meter per second squared (m/s²).
Negative acceleration (velocity decreases).
Total Distance / Total Time.
(Initial Velocity + Final Velocity) / 2 (for uniform acceleration).
Device that measures distance travelled by an automobile.
Device that measures instantaneous speed.
Gives speed.
Gives acceleration.
Gives displacement.
v = u + at.
s = ut + ½at².
2as = v² - u².
Motion under gravity alone (g = 9.8 m/s²). Uniform acceleration.
Motion along a circular path.
Circular motion with constant speed (but changing velocity).
Uniform circular motion is an accelerated motion due to change in direction.
Multiply by 5/18.
Multiply by 18/5.
Object does not change position with respect to surroundings.
Object changes position with respect to time.
Reference point to describe the position of an object.
The numerical value of a physical quantity.
Indicates motion in the opposite direction.
Gives Change in Velocity.
Approx 340 m/s in air.
3 × 108 m/s.
Time taken to complete one revolution.
Second (s).
Formula for speed in uniform circular motion.
Velocity at t=0. 0 if starting from rest.
Velocity at time t. 0 if coming to rest.
Motion in a straight line.
Rate of change of angular displacement.
Another term for retardation.
Covering same distance every second.
Object is at rest.
Constant velocity (zero acceleration).
Velocity at a specific instant of time.
Velocity of one object with respect to another.