Physics XI - Chapter 03: Motion in a Straight Line
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- Motion: Change in position of an object with time relative to a reference point.
- Distance: Total path length (scalar). Displacement: Shortest straight-line distance from initial to final position (vector).
- Speed: Rate of change of distance (scalar). Velocity: Rate of change of displacement (vector).
- Acceleration: Rate of change of velocity. a = (v - u)/t (vector).
- Uniform Motion: Equal displacements in equal time intervals (constant velocity).
- Non-uniform Motion: Unequal displacements in equal time intervals (variable velocity).
- Equations of Motion (Constant Acceleration):
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- sₙ = u + a/2(2n - 1) [Distance in nth second]
- Free Fall: Motion under gravity (a = +g downwards). For upward motion: a = -g.
- Graphical Analysis:
- Slope of position-time graph = Velocity
- Slope of velocity-time graph = Acceleration
- Area under velocity-time graph = Displacement
- Area under acceleration-time graph = Change in velocity
- Relative Velocity: Velocity of object A with respect to B is v_AB = v_A - v_B.
- Important Values: g = 9.8 m/s² (approx. 10 m/s² for calculations).
- Key Points for Vertical Motion:
- At maximum height: velocity = 0
- Time of ascent = Time of descent
- Total time of flight = 2u/g
- Maximum height = u²/2g
- Sign Convention: Typically, upward positive for vertical motion; right positive for horizontal motion.
Basic Level Questions
Chapter Summary
This chapter introduces us to the fundamental concepts of kinematics - the branch of physics that describes motion without considering its causes. We begin by understanding the difference between distance (scalar) and displacement (vector), and between speed (scalar) and velocity (vector). These distinctions are crucial as they form the foundation for all subsequent analysis of motion.
The core of this chapter lies in understanding uniformly accelerated motion and its three fundamental equations. These equations allow us to predict future position, velocity, and time for objects moving with constant acceleration. A special case of this is free fall under gravity, where we apply these equations with a = ±g. Graphical methods provide powerful visual tools to analyze motion, where slopes and areas under curves give us instantaneous velocity, acceleration, and displacement.
Mastering this chapter is essential as it forms the basis for understanding more complex motions in two and three dimensions. The concepts of relative velocity help us understand motion from different frames of reference, a skill that becomes increasingly important in advanced physics. Remember to pay special attention to sign conventions and the vector nature of displacement, velocity, and acceleration when solving problems.