Ch 3 rigorously defines position, displacement, velocity (average and instantaneous), and acceleration using calculus. It covers equations of uniformly accelerated motion and relative velocity.
Position: location on a reference axis. Displacement: change in position (vector, can be negative). Velocity: rate of change of position. Average velocity = Δx/Δt. Instantaneous velocity v = dx/dt (slope of x-t graph). Acceleration: rate of change of velocity. a = dv/dt = d²x/dt².
For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s_n = u + a(2n−1)/2. Graphical interpretation: slope of x-t = velocity; slope of v-t = acceleration; area under v-t curve = displacement. Free fall: a = g = 9.8 m/s² downward.
Download: https://ncert.nic.in/textbook/pdf/keph103.pdf | Part I: https://ncert.nic.in/textbook/pdf/keph1ps.zip
Average velocity is displacement divided by total time interval — it gives an overall sense of motion. Instantaneous velocity is the velocity at a specific instant, obtained by taking the limit as Δt → 0 (derivative dx/dt). Average velocity can be zero for a round trip, but instantaneous velocity is non-zero during the motion.
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