Motion in one dimension
Kinematics Motion in one dimension
Key Terms
- Position (\(x\)): Describes the location of an object along a straight line.
- Displacement (\(Δx\)): The change in position of an object. Formula:
Δx = xfinal - xinitial. - Velocity (\(v\)): The rate of change of displacement. Formula:
v = Δx / Δt. - Acceleration (\(a\)): The rate of change of velocity. Formula:
a = Δv / Δt.
Equations of Motion
For uniformly accelerated motion:
v = u + ats = ut + (1/2)at2v2 = u2 + 2ass = (u + v)/2 × t
Free Fall
A special case where the object moves under the influence of gravity:
- Acceleration due to gravity:
g = 9.8 m/s2. - Upward motion: Deceleration by
g. - Downward motion: Acceleration by
g.
Example Problem
Problem: A car starts from rest and accelerates uniformly at 2 m/s2 for 5 seconds. What is the car’s velocity and displacement?
Solution:
- Given:
u = 0,a = 2 m/s2,t = 5 s. - Final velocity:
v = u + at = 0 + (2)(5) = 10 m/s. - Displacement:
s = ut + (1/2)at2 = 0 + (1/2)(2)(52) = 25 m.
Related Links