Class 11 Physics Chapter 3 | Motion in a Straight Line Full Chapter NCERT Solutions

Motion in a Straight Line: Kinematics of One-Dimensional Motion

Kinematics is the branch of mechanics that describes the motion of objects without considering the causes of motion (forces). This chapter in CBSE Class 11 Physics introduces the fundamental concepts of position, displacement, velocity, and acceleration for objects moving along a straight line. Students learn to describe motion using equations of motion, interpret displacement-time and velocity-time graphs, and apply these concepts to real-world scenarios. Understanding motion in one dimension provides the essential foundation for studying motion in two and three dimensions, as well as for understanding the underlying principles of calculus — differentiation and integration — in a physical context.

Position is the location of an object relative to a chosen reference point or origin. Displacement is the change in position — it is a vector quantity that has both magnitude and direction. The SI unit of displacement is the metre (m). Distance travelled, unlike displacement, is a scalar quantity that measures the total length of the path taken, regardless of direction. An object moving from point A to B and back to A has zero displacement but non-zero distance travelled. Velocity is the rate of change of displacement with respect to time. Average velocity = total displacement / total time, while instantaneous velocity is the velocity at a specific instant. Speed is the magnitude of velocity — it is a scalar quantity. Acceleration is the rate of change of velocity with respect to time = dv/dt. Uniform acceleration occurs when the acceleration is constant, meaning the velocity changes by equal amounts in equal intervals of time. The three equations of motion for uniformly accelerated motion are: v = u + at, s = ut + ½at², and v² = u² + 2as, where u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement. These equations neglect air resistance and assume constant acceleration.

Graphical analysis is a powerful tool for understanding motion. A displacement-time graph has time on the x-axis and displacement on the y-axis. The slope of this graph at any point gives the instantaneous velocity. A horizontal line (zero slope) means the object is stationary. A straight line with constant slope means uniform velocity. A curved line indicates acceleration. A velocity-time graph has time on the x-axis and velocity on the y-axis. The slope of the v-t graph gives acceleration. The area under the v-t graph gives the displacement of the object. For uniformly accelerated motion, the v-t graph is a straight line. If the line has a positive slope, the object is accelerating in the positive direction; if negative slope, it is decelerating. If the line crosses the time axis from positive to negative, the object has reversed direction. The chapter also covers relative velocity — the velocity of one object as measured from another moving object. The relative velocity of A with respect to B is vAB = vA − vB. This concept is crucial for understanding overtaking, crossing, and pursuit problems. For objects moving in the same direction, the relative velocity is the difference of their speeds. For objects moving in opposite directions, the relative velocity is the sum of their speeds. The chapter introduces the concept of instantaneous velocity and acceleration using the limiting process, where the time interval approaches zero. This naturally leads to differential calculus: v = lim(Δt→0) Δx/Δt = dx/dt, and a = dv/dt = d²x/dt². Integration is the inverse process: given acceleration as a function of time, integration gives velocity, and integration of velocity gives displacement. v = u + ∫a·dt, and s = ∫v·dt.

• Displacement is a vector (change in position); distance is a scalar (total path length). Average velocity = displacement/time.
• Uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
• Graphically: s-t graph slope gives velocity; v-t graph slope gives acceleration, v-t graph area gives displacement.
• Relative velocity vAB = vA − vB; same direction means subtract speeds, opposite directions means add speeds.
• Instantaneous velocity v = dx/dt and acceleration a = dv/dt connect kinematics to calculus through limits.