Motion in One Dimension

Everything around us is in motion -- buses on the streets of Kathmandu, the Trisuli River flowing south, even the Earth spinning. Understanding motion mathematically is the first step in physics.

Distance vs. Displacement

• Distance is the total path length traveled. Always positive. A scalar quantity.
• Displacement is the shortest straight-line distance from start to finish with direction. A vector quantity.

Example: Walk 3 km east then 4 km north. Distance = 7 km, but displacement = 5 km northeast (by Pythagoras).

Speed vs. Velocity

• Speed = distance / time (scalar)
• Velocity = displacement / time (vector)

Acceleration

a = (v - u) / t where u = initial velocity, v = final velocity, t = time

If an object slows down, acceleration is negative (deceleration).

Equations of Motion (Uniform Acceleration)

1. v = u + at

2. s = ut + (1/2)at^2

3. v^2 = u^2 + 2as

Worked Examples

Example 1: A bus starts from rest, accelerates at 2 m/s^2 for 10 seconds. Final velocity?

v = 0 + 2 x 10 = 20 m/s

Example 2: A motorcycle at 20 m/s brakes to rest in 4 seconds. Distance covered?

a = (0-20)/4 = -5 m/s^2

s = 20(4) + (1/2)(-5)(16) = 80 - 40 = 40 m

Free Fall

Objects falling under gravity accelerate at approximately g = 9.8 m/s^2 (often rounded to 10 m/s^2).

Nepal Connection: On winding roads from Kathmandu to Pokhara, drivers constantly accelerate and decelerate. Understanding these physics concepts helps engineers design safer roads with proper speed limits.

Key Takeaways

• Distance is scalar; displacement is vector
• The three equations of motion apply to uniform acceleration
• For free fall, use a = g = 9.8 m/s^2 downward
• Always identify u, v, a, t, and s before choosing an equation