Motion in a Straight Line
Displacement, velocity, acceleration, and graphical and equation-based analysis. (Physics › Kinematics, NEET UG syllabus.)
What is Motion in a Straight Line?
The location of an object with respect to a chosen reference point (origin) in a coordinate system.
Key formula / rule: Average Velocity
Key points
- Define and differentiate between position, path length, and displacement.
- Distinguish between speed and velocity, and average and instantaneous values.
- Define acceleration and understand its types (average, instantaneous, uniform).
- Derive and apply the equations of motion for uniformly accelerated motion.
Common exam trap
Confusing distance with displacement, especially in problems involving turns or return journeys.
Definitions
- Term
Position
- Meaning
The location of an object with respect to a chosen reference point (origin) in a coordinate system.
- Term
Path Length (Distance)
- Meaning
The total length of the actual path covered by an object during its motion. It is a scalar quantity and is always non-negative.
- Term
Displacement
- Meaning
The change in position of an object. It is the shortest straight-line distance between the initial and final positions, along with its direction. It is a vector quantity and can be positive, negative, or zero.
- Term
Speed
- Meaning
The rate at which an object covers distance. It is the magnitude of velocity and is a scalar quantity.
- Term
Velocity
- Meaning
The rate of change of an object's displacement. It is a vector quantity, having both magnitude (speed) and direction.
- Term
Acceleration
- Meaning
The rate of change of an object's velocity. It is a vector quantity, indicating how quickly and in what direction the velocity is changing.
Learning objectives
Define and differentiate between position, path length, and displacement.
Distinguish between speed and velocity, and average and instantaneous values.
Define acceleration and understand its types (average, instantaneous, uniform).
Derive and apply the equations of motion for uniformly accelerated motion.
Analyze motion using position-time, velocity-time, and acceleration-time graphs.
Solve numerical problems involving motion in a straight line.
Formulae
- Name
Average Velocity
- Note
Total displacement divided by total time.
- Expression
vavg = Δx / Δt
- Name
Instantaneous Velocity
- Note
Derivative of position with respect to time.
- Expression
v = dx/dt
- Name
Average Acceleration
- Note
Total change in velocity divided by total time.
- Expression
aavg = Δv / Δt
- Name
Instantaneous Acceleration
- Note
Derivative of velocity with respect to time, or second derivative of position.
- Expression
a = dv/dt = d²x/dt²
- Name
First Equation of Motion
- Note
Relates final velocity, initial velocity, acceleration, and time for constant acceleration.
- Expression
v = u + at
- Name
Second Equation of Motion
- Note
Relates displacement, initial velocity, acceleration, and time for constant acceleration.
- Expression
s = ut + ½at²
- Name
Third Equation of Motion
- Note
Relates final velocity, initial velocity, acceleration, and displacement for constant acceleration.
- Expression
v² = u² + 2as
- Name
Displacement in nth second
- Note
Displacement covered by an object in the 'n'th second of motion with constant acceleration.
- Expression
snth = u + a/2 (2n - 1)
Prerequisites
Basic algebra and arithmetic.
Understanding of vectors (magnitude and direction).
Elementary differentiation and integration concepts.
Coordinate geometry basics.
Common mistakes
Confusing distance with displacement, especially in problems involving turns or return journeys.
Using equations of motion for non-uniform acceleration.
Incorrectly applying sign conventions for displacement, velocity, and acceleration.
Mixing up average speed and average velocity.
Misinterpreting slopes and areas in motion graphs.
Keywords
Kinematics
Rectilinear Motion
Position
Displacement
Distance
Speed
Velocity
Acceleration
Equations of Motion
Uniform Acceleration
Graphs of Motion
Free Fall
Practice preview
A police car starts chasing a speeding car 20 seconds after the speeding car passes a certain point. The speeding car moves at a constant speed of 10 m/s. The police car starts from rest and accelerates uniformly at 2 m/…
hard
A particle starts from rest and moves along a straight line. Its acceleration-time (a-t) graph is shown below. (Graph description: From t=0 to t=2s, acceleration is constant at 5 m/s2. From t=2s to t=4s, acceleration is …
hard
A car travels 100 km to the east in 2 hours and then 50 km to the west in 1 hour. What is the average velocity of the car?…
easy