Summary of Chapter

Summary: Motion in a Straight Line

• Motion in 1D involves objects moving along a straight path (e.g., cars on a highway).
• A particle is treated as a point object with negligible size.

1. Position, Displacement, and Distance

• Position is location of the particle relative to origin.
• Displacement = change in position (vector)
• Distance = total path length (scalar)

2. Speed and Velocity

• Speed is scalar; velocity is vector.
• Average speed = total distance / total time
• Average velocity = displacement / time

3. Instantaneous Quantities

• Instantaneous velocity = $v = \frac{dx}{dt}$
• Instantaneous speed = $|v|$
• Instantaneous acceleration = $a = \frac{dv}{dt}$

4. Equations of Motion (uniform acceleration)

• $v = u + at$
• $s = ut + \frac{1}{2}at^2$
• $v^2 = u^2 + 2as$

5. Graphical Analysis

• Slope of x–t graph = velocity
• Slope of v–t graph = acceleration
• Area under v–t = displacement
• Area under a–t = change in velocity

6. Relative Velocity

• Velocity of A relative to B: $v_{AB} = v_A - v_B$
• Opposite direction: $v_{rel} = v_A + v_B$

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This chapter builds your foundation in kinematics, essential for understanding advanced topics like projectile motion and Newton’s laws.