This MCQ module is based on: Speed, Velocity and Acceleration
TOPIC 12 OF 50
Speed, Velocity and Acceleration
🎓 Class 9
Science
CBSE
Theory
Ch 4 — Describing Motion Around Us
⏱ ~15 min
🌐 Language: [gtranslate]
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Recap & The Need for Velocity
In Part 1, we built up speed as a measure of "how fast" something is moving. But "fast" alone is incomplete — a passenger jet flying north and a passenger jet flying east at the same 900 km/h have the same speed but very different effects (one might land in Delhi, the other in Kolkata!). To capture both magnitude and direction, we need a vector cousin of speed: velocity.
4.6 Velocity — Speed With Direction
Velocity is defined as the rate of change of displacement. It carries both a number and a direction.
\[\text{Velocity} = \dfrac{\text{Displacement}}{\text{Time taken}}, \qquad v = \dfrac{s}{t}\]
If the velocity of an object is changing — either in magnitude, in direction, or in both — the motion is non-uniform. For an object moving in a straight line with changing speed, we use:
\[\text{Average velocity} = \dfrac{\text{Total displacement}}{\text{Total time}}\]
For uniformly changing speed (linear change), the average velocity equals the arithmetic mean of the initial and final velocities:
\[v_{\text{avg}} = \dfrac{u + v}{2}\]
where \(u\) is initial velocity and \(v\) is final velocity. This shortcut works only when acceleration is uniform.
Speed vs Velocity at a glance: Speed = |path length| / time (scalar, always ≥ 0). Velocity = displacement / time (vector, may be negative or zero). The magnitude of velocity equals speed only if motion is along a straight line in one direction.
4.7 Acceleration — When Velocity Changes
If you press the accelerator pedal of a car, its velocity grows. Press the brake and the velocity falls. In both cases the velocity is changing with time, and we say the car is accelerating. Acceleration is the heart of all motion problems in this chapter.
\[a = \dfrac{\text{change in velocity}}{\text{time taken}} = \dfrac{v - u}{t}\]
where \(u\) = initial velocity, \(v\) = final velocity, \(t\) = time interval. The SI unit is metre per second squared (m/s²).
Sign of Acceleration
| Situation | Sign of \(a\) | Meaning |
|---|---|---|
| \(v > u\) (speeding up in +ve direction) | Positive (+) | Acceleration in direction of motion |
| \(v < u\) (slowing down) | Negative (−) | Retardation / deceleration; opposite to motion |
| \(v = u\) (constant velocity) | Zero | Uniform motion — no acceleration |
Caution: A negative acceleration does not always mean an object is slowing down. It just means the acceleration vector points in the negative direction of the chosen axis. If the object is also moving in the negative direction, a negative acceleration actually speeds it up!
Uniform vs Non-Uniform Acceleration
Acceleration is uniform if it stays constant in both magnitude and direction (e.g., a freely falling apple near Earth has \(a = 9.8\) m/s² downwards throughout). It is non-uniform if either changes (e.g., a car driver tapping the accelerator unevenly during city traffic).
📈 Read the v–t Graph — Step through each shape L3 Apply
A velocity–time graph tells the whole story of motion. Click each plot to read what its shape reveals about acceleration. Apply the rule: slope of v–t graph = acceleration.
Click either graph above to step through how its shape encodes acceleration.
Activity 4.2 — Acceleration of a Bus
L3 Apply
Predict: A school bus starts from rest and reaches 36 km/h in 10 s. Will the magnitude of its acceleration be more than, less than, or equal to 1 m/s²?
- Note initial velocity \(u = 0\).
- Convert final velocity: \(36 \text{ km/h} = 10\) m/s.
- Use \(a = (v-u)/t\) and compute.
\(a = (10-0)/10 = 1\) m/s². The bus speeds up by 1 metre per second every second. This is uniform acceleration if the same change continues each second.
Worked Numerical Examples
Example 1 — Bicycle accelerating
A cyclist starts from rest and reaches a velocity of 6 m/s in 30 s. Find his acceleration.
Given: \(u = 0\), \(v = 6\) m/s, \(t = 30\) s.
\(a = \dfrac{v-u}{t} = \dfrac{6-0}{30} = 0.2\) m/s².
Answer: 0.2 m/s² (positive — speeding up).
Example 2 — Bus retardation
A bus moving at 72 km/h applies brakes and stops uniformly in 8 s. Find its retardation.
Given: \(u = 72 \text{ km/h} = 20\) m/s, \(v = 0\), \(t = 8\) s.
\(a = \dfrac{0-20}{8} = -2.5\) m/s².
Answer: Acceleration \(= -2.5\) m/s²; retardation \(= 2.5\) m/s².
Example 3 — Train change of velocity
A train accelerates uniformly from 36 km/h to 90 km/h in 1 minute. Compute (a) acceleration and (b) average velocity for the minute.
Given: \(u = 36 \text{ km/h} = 10\) m/s, \(v = 90 \text{ km/h} = 25\) m/s, \(t = 60\) s.
(a) \(a = (25-10)/60 = 0.25\) m/s².
(b) \(v_{\text{avg}} = (u+v)/2 = (10+25)/2 = 17.5\) m/s.
Example 4 — Reversing direction
A ball thrown vertically up leaves the hand at 20 m/s. After 4 s, its velocity is 19.2 m/s downward. Find the average acceleration. (Take upward as positive.)
Given: \(u = +20\) m/s, \(v = -19.2\) m/s, \(t = 4\) s.
\(a = \dfrac{v-u}{t} = \dfrac{-19.2 - 20}{4} = \dfrac{-39.2}{4} = -9.8\) m/s².
Answer: 9.8 m/s² downward — the familiar acceleration due to gravity.
Example 5 — Two-stage motion
A scooter accelerates from 5 m/s to 15 m/s in 4 s, then maintains 15 m/s for the next 6 s. Find the acceleration in each phase.
Phase 1: \(a_1 = (15-5)/4 = 2.5\) m/s².
Phase 2: \(a_2 = (15-15)/6 = 0\) m/s² (uniform motion).
Example 6 — Average velocity from displacement
A particle moves 60 m east in 4 s, then 80 m north in 6 s. Find (a) the magnitude of the displacement and (b) the magnitude of its average velocity over the 10-s journey.
(a) Displacement \(= \sqrt{60^2 + 80^2} = \sqrt{3600+6400} = \sqrt{10000} = 100\) m.
(b) \(|v_{\text{avg}}| = 100 \text{ m} / 10 \text{ s} = 10\) m/s, directed from start to end.
In-Text Question Check
Q. Distinguish between speed and velocity. Can the speed of an object be zero while its velocity is not? Can the velocity be zero while the speed is not?
Speed is scalar; velocity is vector. If speed is zero, the object is not moving, so velocity must also be zero. Conversely, if velocity is zero (no displacement per unit time), then over that interval, no path is being covered, so speed is also zero. The two cannot disagree at the instant of measurement.
Speed is scalar; velocity is vector. If speed is zero, the object is not moving, so velocity must also be zero. Conversely, if velocity is zero (no displacement per unit time), then over that interval, no path is being covered, so speed is also zero. The two cannot disagree at the instant of measurement.
Competency-Based Questions
A car on a highway shows the following readings on its speedometer: at \(t=0\) it reads 18 km/h, and at \(t=5\) s it reads 54 km/h. The driver claims the car has been accelerating uniformly throughout the 5 s.
Q1. The change in velocity in m/s is — L2
(b) 10 m/s. 18 km/h = 5 m/s; 54 km/h = 15 m/s; Δv = 10 m/s.
Q2. The acceleration of the car is — L3
\(a = 10 / 5 = 2\) m/s².
Q3. Average velocity for the 5-s interval is — L3
\(v_{\text{avg}} = (5+15)/2 = 10\) m/s.
Q4. Distance covered in those 5 s equals — L4
Distance = average velocity × time = 10 × 5 = 50 m.
Q5. If the same acceleration continues, after another 5 s the car's velocity will be — L3
\(v = 15 + 2 \times 5 = 25\) m/s = 90 km/h.
Assertion–Reason Questions
Choose: (A) Both true, R explains A. (B) Both true, R does NOT explain A. (C) A true, R false. (D) A false, R true.
Assertion: A body moving with uniform velocity has zero acceleration.
Reason: Acceleration is the rate of change of velocity.
(A) If velocity does not change, its rate of change is zero; R explains A.
Assertion: Negative acceleration always reduces the speed of a body.
Reason: Negative acceleration means deceleration.
(D) A is false: a body moving in the negative direction is sped up by a negative acceleration. R is true only when v and a have opposite signs.
Assertion: A car going around a circular bend at constant speed has zero acceleration.
Reason: Acceleration depends only on the change in speed.
(D) A is false — direction of velocity changes, so acceleration is not zero (it is centripetal). R is false because acceleration depends on change of velocity (vector), not just speed.
Correct option: both A and R are false → among the four options, this matches none exactly; the closest standard board answer is (D) form treating "A false". Mark A false, R false.
Correct option: both A and R are false → among the four options, this matches none exactly; the closest standard board answer is (D) form treating "A false". Mark A false, R false.
Frequently Asked Questions — Velocity and Acceleration
What is velocity and acceleration in Class 9 Science (CBSE/NCERT)?
Velocity and Acceleration is a key topic in NCERT Class 9 Science Chapter 4 — Describing Motion Around Us. It explains speed, velocity and acceleration with their formulas, si units and worked numerical examples for class 9. Core ideas covered include speed, average speed, instantaneous speed, velocity. Mastering this subtopic is essential for scoring well in the CBSE Class 9 Science exam and for building a strong foundation for the Class 10 board exam, because these concepts repeatedly appear in MCQs, short answers and long-answer questions. This part gives a complete, exam-ready explanation with activities, diagrams and competency-based practice aligned to NCERT.
Why is speed important in NCERT Class 9 Science?
Speed is important in NCERT Class 9 Science because it forms the foundation for understanding velocity and acceleration in Chapter 4 — Describing Motion Around Us. Without a clear idea of speed, students cannot answer higher-order CBSE questions involving average speed, instantaneous speed, velocity. School and competitive papers regularly include 2-mark and 3-mark questions on this concept, and competency-based questions often link speed to real-life situations. Building clarity here pays off directly in marks at Class 9 and again in the Class 10 board exam.
How is velocity and acceleration tested in the Class 9 Science CBSE exam?
The CBSE Class 9 Science exam tests velocity and acceleration through a mix of 1-mark MCQs, 2-mark short answers, 3-mark explanations with examples, 5-mark descriptive questions (often with diagrams or derivations) and 4-mark competency-based questions. Expect direct questions on speed, average speed, instantaneous speed and application-based questions drawn from NCERT activities. Students who follow the NCERT Exploration textbook thoroughly and practise this chapter's questions consistently score in the 90%+ range.
What are the key terms to remember for velocity and acceleration in Class 9 Science?
The key terms to remember for velocity and acceleration in NCERT Class 9 Science Chapter 4 are: speed, average speed, instantaneous speed, velocity, average velocity, acceleration. Each of these concepts carries exam weightage and regularly appears in the CBSE Class 9 paper. Write clear one-line definitions of every term in your revision notes and revisit them before the exam. Linking these terms visually through a flowchart or concept map makes recall easier during the Class 9 Science exam.
Is Velocity and Acceleration included in the Class 9 Science syllabus for 2025–26 CBSE?
Yes, Velocity and Acceleration is part of the NCERT Class 9 Science syllabus (2025–26) prescribed by CBSE under the new NCERT Exploration textbook. It falls under Chapter 4 — Describing Motion Around Us — and is examined in the annual paper. The current syllabus retains the full treatment of speed, average speed, instantaneous speed as per the NCERT textbook. Because CBSE bases every Class 9 question on NCERT, studying this part thoroughly ensures complete syllabus coverage and guarantees marks from this chapter.
How should I prepare velocity and acceleration for the CBSE Class 9 Science exam?
Prepare velocity and acceleration for the CBSE Class 9 Science exam in three steps. First, read this NCERT part carefully, highlighting definitions and diagrams of speed, average speed, instantaneous speed. Second, solve every in-text question and end-of-chapter exercise — CBSE questions often come directly from NCERT. Third, practise competency-based and assertion-reason questions to sharpen reasoning. Write answers in the exam-style format (point-wise with diagrams) and time yourself. This method delivers confidence and full marks in the exam.
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