Kinematic Equations for Uniformly Accelerated Motion
Derives and applies the three equations of motion for constant acceleration in one dimension.
What is Kinematic Equations for Uniformly Accelerated Motion?
Motion in a straight line in which the velocity changes by equal amounts in equal intervals of time.
Key formula / rule: First Kinematic Equation
Key points
- To understand the conditions under which the kinematic equations are valid.
- To derive or recall the three kinematic equations for uniformly accelerated motion.
- To apply these equations to solve problems involving one-dimensional motion with constant acceleration.
- To interpret the physical meaning of each term in the equations.
Common exam trap
Applying these equations when acceleration is not constant.
Definitions
- Term
Uniformly Accelerated Motion
- Meaning
Motion in a straight line in which the velocity changes by equal amounts in equal intervals of time.
- Term
Displacement (s)
- Meaning
The change in position of an object. It is a vector quantity and can be positive or negative.
- Term
Initial Velocity (u)
- Meaning
The velocity of an object at the beginning of the time interval considered.
- Term
Final Velocity (v)
- Meaning
The velocity of an object at the end of the time interval considered.
- Term
Acceleration (a)
- Meaning
The rate of change of velocity with respect to time. For uniformly accelerated motion, it is constant.
Learning objectives
To understand the conditions under which the kinematic equations are valid.
To derive or recall the three kinematic equations for uniformly accelerated motion.
To apply these equations to solve problems involving one-dimensional motion with constant acceleration.
To interpret the physical meaning of each term in the equations.
Formulae
- Name
First Kinematic Equation
- Note
Relates final velocity (v), initial velocity (u), acceleration (a), and time (t).
- Expression
v = u + at
- Name
Second Kinematic Equation
- Note
Relates displacement (s), initial velocity (u), acceleration (a), and time (t).
- Expression
s = ut + ½at²
- Name
Third Kinematic Equation
- Note
Relates final velocity (v), initial velocity (u), acceleration (a), and displacement (s).
- Expression
v² = u² + 2as
- Name
Average Velocity (Uniform Acceleration)
- Note
Useful when time is not directly involved or can be easily found.
- Expression
vavg = (u+v)/2
Prerequisites
Understanding of basic concepts of motion (distance, displacement, speed, velocity).
Understanding of acceleration.
Basic algebra and calculus (for derivation, though not required for application).
Common mistakes
Applying these equations when acceleration is not constant.
Incorrectly assigning signs to displacement, velocity, or acceleration.
Confusing initial and final velocities.
Using the wrong equation for the given set of known and unknown variables.
Keywords
Kinematics
Uniform Acceleration
Equations of Motion
Velocity
Displacement
Time
Acceleration
One-dimensional motion
Practice preview
An object starts from rest and accelerates uniformly at 2 m/s². What will be its velocity after 5 seconds?…
easy
A ball is dropped from a height of 45 meters. If it accelerates downwards due to gravity at 10 m/s², how long does it take to reach the ground?…
medium
A particle starts from rest and moves with constant acceleration. If it covers 100 meters in the first 5 seconds, what is the distance it will cover in the next 5 seconds?…
hard