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Physics · Class 11 Science

Ch 2Motion in a Straight Line — Class 11 Physics, concept-first.

Motion is one of the most universal facts of nature. We walk, run, cycle; even while we sleep, air moves in and out of our lungs and blood circulates through our arteries and veins. Leaves fall from trees, water flows down a dam, cars and aircraft carry people from place to place.

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Concepts

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Key concepts

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Instantaneous Velocity

You already know average velocity. If a car travels 120 km in 2 hours, its average velocity is 60 km/h. That tells you the overall rate, but it hides everything that happened in between — the traffic jams, the sudden bur…

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

2.1

Introduction

Motion is one of the most universal facts of nature. We walk, run, cycle; even while we sleep, air moves in and out of our lungs and blood circulates through our arteries and veins.

2.2

Instantaneous Velocity and Speed

Average velocity tells you the overall rate of displacement over a finite time interval. But motion is rarely uniform — a car speeds up, slows down, stops at a light.

+Worked Examplesi1 question
  1. Example 2.1The position of an object moving along x-axis is given by $x = a + bt^{2}$ where $a = 8.5\ \text{m}$, $b = 2.5\ \text{m s}^{-2}$ and $t$ is…Preview
2.3

Acceleration

When an object’s velocity changes — either in magnitude, direction, or both — we say it is accelerating.

2.4

Kinematic Equations for Uniformly Accelerated Motion

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When acceleration is constant, the motion is simple enough that we can write exact relationships between position, velocity, acceleration, and time.

+Worked Examplesi1 question
  1. Example 2.2Obtain equations of motion for constant acceleration using method of calculus.Preview
+Worked Examplesi1 question
  1. Example 2.3A ball is thrown vertically upwards with a velocity of $20\ \text{m s}^{-1}$ from the top of a multistorey building. The height of the point…Preview
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  1. Example 2.5Galileo's law of odd numbers: "The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in…Preview
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  1. Example 2.6Stopping distance of vehicles: When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping dista…Preview
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  1. Example 2.7Reaction time: When a situation demands our immediate action, it takes some time before we really respond. Reaction time is the time a perso…Preview
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  1. Example 2.4Free-fall: Discuss the motion of an object under free fall. Neglect air resistance.Preview

Summary

- Frame of reference: Motion is described relative to a chosen origin and axes. Position is a vector ; in one dimension, it is simply with sign.

Points to Ponder

1. The location of the origin and which direction is called positive along an axis are completely up to you.

Exercises

+Show 18 questions18 questions
  1. 2.1In which of the following examples of motion, can the body be considered approximately a point object: (a) a railway carriage moving without…Free
  2. 2.2The position-time ($x$-$t$) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in F…Free
  3. 2.3A woman starts from her home at 9.00 am, walks with a speed of $5\ \text{km h}^{-1}$ on a straight road up to her office $2.5\ \text{km}$ aw…Free
  4. 2.4A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and…Preview
  5. 2.5A car moving along a straight highway with speed of $126\ \text{km h}^{-1}$ is brought to a stop within a distance of $200\ \text{m}$. What…Preview
  6. 2.6A player throws a ball upwards with an initial speed of $29.4\ \text{m s}^{-1}$. (a) What is the direction of acceleration during the upward…Preview
  7. 2.7Read each statement below carefully and state with reasons and examples, if it is true or false; A particle in one-dimensional motion (a) wi…Preview
  8. 2.8A ball is dropped from a height of $90\ \text{m}$ on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot…Preview
  9. 2.9Explain clearly, with examples, the distinction between: (a) magnitude of displacement (sometimes called distance) over an interval of time,…Preview
  10. 2.10A man walks on a straight road from his home to a market $2.5\ \text{km}$ away with a speed of $5\ \text{km h}^{-1}$. Finding the market clo…Preview
  11. 2.11In Exercises 2.9 and 2.10, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is n…Preview
  12. 2.12Look at the graphs (a) to (d) (Fig. 2.10) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion…Preview
  13. 2.13Figure 2.11 shows the $x$-$t$ plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a…Preview
  14. 2.14A police van moving on a highway with a speed of $30\ \text{km h}^{-1}$ fires a bullet at a thief's car speeding away in the same direction…Preview
  15. 2.15Suggest a suitable physical situation for each of the following graphs (Fig 2.12): ![Figure 2.12](/figures/motion-in-a-straight-line/three-g…Preview
  16. 2.16Figure 2.13 gives the $x$-$t$ plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more…Preview
  17. 2.17Figure 2.14 gives the $x$-$t$ plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which inte…Preview
  18. 2.18Figure 2.15 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which i…Preview

NCERT Exemplar

Higher-order thinking problems from the NCERT Exemplar.

+Show 26 questions26 questions
  1. Q1Four position-time ($x$ versus $t$) graphs of a particle moving along a straight line are described below. In only ONE of them can the avera…Free
  2. Q2A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all q…Free
  3. Q3In one dimensional motion, instantaneous speed $v$ satisfies $0 \le v < v_0$. (a) The displacement in time $T$ must always take non-negative…Free
  4. Q4A vehicle travels half the distance $L$ with speed $V_1$ and the other half with speed $V_2$, then its average speed is (a) $\dfrac{V_1 + V_…Preview
  5. Q5The displacement of a particle is given by $x = (t - 2)^2$ where $x$ is in metres and $t$ in seconds. The distance covered by the particle i…Preview
  6. Q6At a metro station, a girl walks up a stationary escalator in time $t_1$. If she remains stationary on the escalator, then the escalator tak…Preview
  7. Q7The variation of a quantity $A$ with a quantity $B$ describes the motion of a particle along a straight line. When $A$ (vertical axis) is pl…Preview
  8. Q8The position–time ($x$ versus $t$) graph of a particle moving in a straight line has the following shape, reading left to right. It begins a…Preview
  9. Q9For the one-dimensional motion, described by $x = t - \sin t$ (Note: more than one of the given options may be correct.) (a) $x(t) > 0$ for…Preview
  10. Q10A spring with one end attached to a mass and the other to a rigid support is stretched and released. (Note: more than one of the given optio…Preview
  11. Q11A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls.…Preview
  12. Q12Four position-time ($x$ versus $t$) graphs of a particle moving along a straight line are described below. Graph (a): at $t=0$ the position…Preview
  13. Q13A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its accelerati…Preview
  14. Q14Give examples of a one-dimensional motion where (a) the particle moving along positive $x$-direction comes to rest periodically and moves fo…Preview
  15. Q15Give example of a motion where $x > 0$, $v < 0$, $a > 0$ at a particular instant.Preview
  16. Q16An object falling through a fluid is observed to have acceleration given by $a = g - bv$ where $g$ = gravitational acceleration and $b$ is c…Preview
  17. Q17A ball is dropped from rest above the ground and bounces repeatedly. Its displacement $x$ (measured upward from the ground, all quantities t…Preview
  18. Q18A particle executes the motion described by $x(t) = x_0\left(1 - e^{-\gamma t}\right)$; $t \ge 0$, $x_0 > 0$. (a) Where does the particle st…Preview
  19. Q19A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of 18 m/h while the…Preview
  20. Q20A man runs across the roof-top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is…Preview
  21. Q21A ball is dropped from a building of height 45 m. Simultaneously another ball is thrown up with a speed 40 m/s. Calculate the relative speed…Preview
  22. Q22The velocity–displacement graph of a particle is a straight line: the velocity has its maximum value $v_0$ on the velocity axis when the dis…Preview
  23. Q23It is a common observation that rain clouds can be at about a kilometre altitude above the ground. (a) If a rain drop falls from such a heig…Preview
  24. Q24A motor car moving at a speed of 72 km/h can not come to a stop in less than 3.0 s while for a truck this time interval is 5.0 s. On a higwa…Preview
  25. Q25A monkey climbs up a slippery pole for 3 seconds and subsequently slips for 3 seconds. Its velocity at time $t$ is given by $v(t) = 2t(3 - t…Preview
  26. Q26A man is standing on top of a building 100 m high. He throws two balls vertically, one at $t = 0$ and other after a time interval (less than…Preview