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Class 11 Physics Notes

Motion in a Straight Line Notes

Covers distance, displacement, velocity, acceleration, and the equations of motion for objects moving along a line, as per CBSE, JEE, and NEET syllabi.

Class11SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is motion in a straight line in one line?

It is the study of one-dimensional (rectilinear) motion using the quantities distance, displacement, speed, velocity, and acceleration, linked by the kinematic equations v = u + at, s = ut + ½at², and v² = u² + 2as.

Distance and Displacement

Distance is the total path length covered by an object during its motion. It is a scalar quantity and is always positive, never decreasing with time.Displacement is the shortest straight-line distance between the initial and final positions, along with direction. It is a vector quantity and can be positive, negative, or zero.

Key point

Magnitude of displacement ≤ distance travelled. The two are equal only when motion is along a straight line without any change in direction.

Speed and Velocity

Average speed = total distance / total time taken. Average velocity = total displacement / total time taken.Instantaneous velocity is the limiting value of average velocity as the time interval approaches zero, i.e., the derivative of position with respect to time: v = dx/dt.

Key point

Average speed can be greater than the magnitude of average velocity if the path is not straight, but instantaneous speed always equals the magnitude of instantaneous velocity.

Acceleration

Acceleration is the rate of change of velocity with time: a = dv/dt. Average acceleration = change in velocity / time taken.If velocity increases with time, acceleration is positive (in the direction of motion); if velocity decreases, acceleration is negative (retardation).

a=dvdt=d2xdt2a = \dfrac{dv}{dt} = \dfrac{d^2x}{dt^2}
Instantaneous acceleration

Equations of Motion (Uniform Acceleration)

For an object moving with constant acceleration a, starting with initial velocity u, these three equations connect velocity, displacement, and time.

v=u+atv = u + at
First equation of motion
s=ut+12at2s = ut + \dfrac{1}{2}at^2
Second equation of motion
v2=u2+2asv^2 = u^2 + 2as
Third equation of motion

Exam tip

These equations apply only when acceleration is constant. For variable acceleration, calculus (integration/differentiation) must be used instead.

Motion Graphs

On a position-time graph, the slope at any point gives instantaneous velocity. A straight line indicates uniform velocity; a curved line indicates changing velocity.On a velocity-time graph, the slope gives acceleration, and the area under the curve gives displacement. A straight horizontal line means zero acceleration; a straight sloped line means uniform acceleration.

Key point

Area under a v-t graph between two time instants gives displacement, including sign — area below the time axis represents negative displacement.

Relative Velocity

Relative velocity of object A with respect to object B is the velocity of A as observed from B, calculated as the vector difference: v_AB = v_A − v_B.For motion along the same line, if both move in the same direction, relative velocity is the difference of their speeds; if in opposite directions, it is the sum.

vAB=vA−vBv_{AB} = v_A - v_B
Relative velocity of A with respect to B

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Average velocity

vˉ=ΔxΔt\bar{v} = \dfrac{\Delta x}{\Delta t}

Displacement over time interval

Average acceleration

aˉ=ΔvΔt\bar{a} = \dfrac{\Delta v}{\Delta t}

Change in velocity over time interval

First equation of motion

v=u+atv = u + at

Constant acceleration only

Second equation of motion

s=ut+12at2s = ut + \dfrac{1}{2}at^2

Third equation of motion

v2=u2+2asv^2 = u^2 + 2as

Distance in nth second

sn=u+a2(2n−1)s_n = u + \dfrac{a}{2}(2n - 1)

Useful for discrete-second problems

Relative velocity

vAB=vA−vBv_{AB} = v_A - v_B

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • CBSE board exams frequently ask for derivations of the three equations of motion using both graphical and calculus methods — practice both.
  • CBSE numericals often combine displacement-in-nth-second with average velocity or graph interpretation questions.
  • JEE Main/Advanced favor relative velocity problems (two trains, rain-man, boat-river) and v-t graph area calculations, sometimes with variable acceleration requiring calculus.
  • NEET tends to test direct application of the three equations of motion and free-fall (gravity as constant acceleration) numericals with less graph-heavy analysis.
  • A common trap across all three exams: confusing distance with displacement when acceleration reverses direction mid-motion (e.g., a ball thrown up and coming down) — total distance and net displacement differ in such cases.

Solved problems

Worked examples

JEE / NEET-style numericals, solved step by step.

1

Finding displacement from a v-t graph

A car moving with an initial velocity of 5 m/s accelerates uniformly at 2 m/s² for 4 seconds. Find its velocity after 4 s and the displacement covered.

  1. Given: u = 5 m/s, a = 2 m/s², t = 4 s
  2. Using v = u + at: v = 5 + (2)(4) = 13 m/s
  3. Using s = ut + ½at²: s = (5)(4) + ½(2)(16) = 20 + 16 = 36 m

Answer

v=13 m/s,s=36 mv = 13\ \text{m/s}, \quad s = 36\ \text{m}
2

Relative velocity of two trains

Two trains A and B are moving on parallel tracks in the same direction with speeds 72 km/h and 54 km/h respectively. Find the velocity of A relative to B.

  1. Convert speeds to m/s: v_A = 72 × (5/18) = 20 m/s, v_B = 54 × (5/18) = 15 m/s
  2. Since both move in the same direction, v_AB = v_A − v_B
  3. v_AB = 20 − 15 = 5 m/s (in the direction of A's motion)

Answer

vAB=5 m/sv_{AB} = 5\ \text{m/s}

FAQ

Common questions

What is the difference between speed and velocity?

Speed is a scalar quantity indicating how fast an object moves, while velocity is a vector quantity that includes both magnitude and direction. Speed is always positive; velocity can be negative depending on direction.

Can an object have zero velocity but non-zero acceleration?

Yes. For example, a ball thrown vertically upward has zero velocity at its highest point, but acceleration due to gravity (9.8 m/s²) continues to act on it throughout its flight.

Do the equations of motion apply to motion under gravity?

Yes, since acceleration due to gravity is constant near Earth's surface, all three equations of motion apply directly, with a replaced by g (taking sign convention based on direction of motion).

Why is displacement sometimes zero even when distance is not?

Displacement depends only on the initial and final positions. If an object returns to its starting point after moving, the net displacement is zero even though the distance travelled is non-zero.

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Related notes

All Class 11 Physics NotesLaws of Motion NotesMotion in a Plane Notes

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