CBSE Class 11 Physics Chapter 3 Notes: Motion in a Straight Line

Key Definitions in Motion

Distance

The total path length covered by an object between its initial and final positions. It is a scalar quantity and is always non-negative.

Displacement

The shortest straight-line distance between the initial and final positions of an object, along with its direction. It is a vector quantity and can be positive, negative, or zero.

Speed

The rate at which an object covers distance. It is a scalar quantity (distance/time). Average speed = Total distance / Total time.

Velocity

The rate at which an object changes its displacement. It is a vector quantity (displacement/time). Average velocity = Total displacement / Total time. Instantaneous velocity is the velocity at a particular instant.

Acceleration

The rate of change of velocity of an object. It is a vector quantity (change in velocity / time). Average acceleration = (v - u) / t. Instantaneous acceleration is the acceleration at a particular instant.

Uniform Motion

Motion where an object covers equal distances in equal intervals of time along a straight line. Velocity is constant, and acceleration is zero.

Non-uniform Motion

Motion where an object covers unequal distances in equal intervals of time, or equal distances in unequal intervals of time. Velocity changes with time, implying non-zero acceleration.

Distance vs. Displacement & Speed vs. Velocity

Understanding Graphical Analysis of Motion

Graphical analysis is a powerful tool to describe motion in a straight line. Position-time graphs (x-t graphs) show an object's position at different times. The slope of an x-t graph gives the velocity of the object. A straight line with a positive slope indicates uniform positive velocity, a straight line with a negative slope indicates uniform negative velocity, and a horizontal line means the object is at rest (zero velocity). A curved x-t graph indicates non-uniform velocity, meaning acceleration is present. The slope of the tangent at any point on a curved x-t graph gives the instantaneous velocity.

Velocity-time graphs (v-t graphs) illustrate how an object's velocity changes over time. The slope of a v-t graph represents the acceleration of the object. A horizontal line in a v-t graph signifies uniform velocity (zero acceleration). A straight line with a positive slope indicates uniform positive acceleration, while a negative slope shows uniform negative acceleration (retardation). The area under the v-t graph gives the displacement of the object. For areas above the time axis, displacement is positive; for areas below, it's negative. The total area gives the net displacement.

Finally, Acceleration-time graphs (a-t graphs) show how acceleration changes with time. The area under an a-t graph represents the change in velocity over a given time interval. These graphical interpretations are vital for qualitative and quantitative analysis of motion and are frequently tested in exams.

Key Formulas and Equations of Motion

• Equations of Motion (for uniformly accelerated motion):
• 1. v = u + at (Velocity-time relation)
• 2. s = ut + (1/2)at² (Position-time relation)
• 3. v² = u² + 2as (Position-velocity relation)
• Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.
• Displacement in n-th second: s_n = u + (a/2)(2n - 1)
• Relative Velocity (1D): v_AB = v_A - v_B (Velocity of A with respect to B). Apply sign conventions consistently.
• Free Fall: When an object falls under gravity, a = g (positive if downward is positive) or a = -g (if upward is positive). For upward projection, initial velocity u is positive, and a = -g (always directed downwards).
• Sign Convention: Choose a direction (e.g., upward or rightward) as positive and stick to it for all vector quantities (displacement, velocity, acceleration).
• Slope of x-t graph gives velocity. Slope of v-t graph gives acceleration. Area under v-t graph gives displacement.

Worked Example: Applying Equations of Motion

• Example: A car starting from rest accelerates uniformly at 2 m/s² for 10 seconds. Calculate the distance covered and its final velocity.
• Solution: Given: u = 0 m/s (starts from rest), a = 2 m/s², t = 10 s. To find final velocity v: Using v = u + at v = 0 + (2 m/s²)(10 s) v = 20 m/s To find distance covered s: Using s = ut + (1/2)at² s = (0)(10) + (1/2)(2 m/s²)(10 s)² s = 0 + (1)(100) s = 100 m The car covers a distance of 100 m and achieves a final velocity of 20 m/s.

Exam Trap & Scoring Tip!

Students often confuse scalar and vector quantities, especially when dealing with distance/displacement and speed/velocity. Always pay attention to direction for vector quantities. In problems involving free fall or vertical motion, correctly choosing a consistent sign convention for g, initial velocity u, and final velocity v, and displacement s is critical. A common mistake is using g as positive when an object is thrown upwards, which is incorrect if upward is taken as positive. Remember, g always acts downwards! Also, carefully read whether the question asks for average speed or average velocity, as their calculation methods differ significantly.

Practice Questions with Solutions

• Q: Can an object have zero velocity but non-zero acceleration? A: Yes. An object momentarily at rest (zero velocity) at its highest point during vertical throw still experiences acceleration due to gravity (g).
• Q: What does the area under a velocity-time graph represent? A: The area under a velocity-time graph represents the displacement of the object during that time interval. If asking for total distance, sum the magnitudes of areas.
• Q: A car travels 50 km East, then 50 km West. What is its displacement and distance covered? A: Distance covered = 50 km + 50 km = 100 km. Displacement = 0 km (returns to starting point).
• Q: State the condition under which the three equations of motion are valid. A: The three equations of motion (v = u + at, s = ut + (1/2)at², v² = u² + 2as) are valid only when the acceleration is constant (uniform acceleration) and motion is along a straight line.

Frequently Asked Questions