- Dr.Sanjaykumar Pawar
Uniformly Accelerated Motion (1-D) Physics Notes, Formulas & NEET Questions
 |
| Uniformly Accelerated Motion (1-D): Equations of Motion, Graphs and NEET Physics Concepts |
Internal Links
1. Motion in One Dimension Foundation
Motion in One Dimension Class 11 Physics Notes
Before introducing uniformly accelerated motion, link readers to the basic concepts of displacement, velocity and speed.
2. Instantaneous Velocity & Acceleration
Instantaneous Velocity and Acceleration Explained
NCERT Physics Class 11 Chapter 2: Instantaneous Velocity & Acceleration
Under "Important Terms" section after explaining acceleration.
3. Vectors in Physics
Vectors Class 11 Physics Notes
CBSE Class 11 Physics Vectors Notes, MCQs, Questions & Answers | NEET Preparation
explaining displacement as a vector quantity.
4. Newton's Laws of Motion
Newton's Laws of Motion Class 11 Physics
Block and Trolley System NEET Solution | Acceleration & Tension Explained
acceleration concepts because force causes acceleration.
5. Free Fall Motion
Free Fall and Acceleration Due to Gravity
NEET Tips section where free fall problems are mentioned.
6. Graphical Motion Analysis
Velocity-Time and Acceleration-Time Graphs
diagram-based questions.
Uniform acceleration formula
Equations of motion derivation
Motion in one dimension notes
Class 11 Physics chapter 2 notes
NEET physics motion questions
JEE physics kinematics notes
Velocity time graph questions
Acceleration numericals with solutions
CBSE Physics important questions
Physics revision notes for NEET
FAQ Schema Questions
Q1. What is uniformly accelerated motion?
Uniformly accelerated motion is motion in which acceleration remains constant with time.
Q2. What are the three equations of motion?
The three equations are v = u + at, s = ut + ½at² and v² = u² + 2as.
Q3. What does the slope of a velocity-time graph represent?
The slope of a velocity-time graph represents acceleration.
Q4. What does the area under a velocity-time graph represent?
The area represents displacement.
Q5. Is uniformly accelerated motion important for NEET and JEE?
Yes, it is a fundamental topic used in many mechanics problems.
Uniformly Accelerated Motion (1-D)
1. Meaning of Uniformly Accelerated Motion
Uniformly accelerated motion means an object is moving in a straight line and its acceleration remains constant with time.
- The velocity changes by the same amount in equal intervals of time.
- The motion takes place in one dimension.
Example: A bike increases its speed by 5 m/s every second.
Important Terms
1. Initial Velocity (u)
Initial velocity is the velocity of an object at the starting time. It is represented by u.
At starting time:
t = 0, velocity = u
2. Final Velocity (v)
Final velocity is the velocity of an object after a certain time. It is represented by v.
3. Acceleration (a)
Acceleration is the rate of change of velocity.
Unit of acceleration = m/s²
4. Displacement (s)
Displacement is the distance travelled by an object in a particular direction.
Unit = metre (m)
First Equation of Motion
Derivation:
Acceleration:
a = dv/dt
Rearranging:
a dt = dv
Integrating:
∫a dt = ∫dv
a(t - 0) = v - u
at = v - u
Final velocity = Initial velocity + Change in velocity
Second Equation of Motion
Derivation:
Velocity:
v = ds/dt
Therefore:
ds = v dt
Using:
v = u + at
ds = (u + at)dt
After integration:
Displacement = Distance due to initial velocity + Distance due to acceleration
Third Equation of Motion
Derivation:
From first equation:
v = u + at
Rearranging:
t = (v - u)/a
Using second equation:
s = ut + 1/2 at²
After simplification:
This equation is useful when time is not given.
Three Equations of Motion Summary
1. Velocity Equation
Used to find final velocity when time is given.
2. Displacement Equation
Used to find displacement when time is given.
3. Time Independent Equation
Used when time is not given.
Easy Memory Trick
- V-U-AT: v = u + at
- S-U-T-A-T: s = ut + 1/2 at²
- V-U-AS: v² = u² + 2as
Symbols at a Glance
| Symbol | Meaning | Unit |
|---|---|---|
| u | Initial Velocity | m/s |
| v | Final Velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | second |
| s | Displacement | metre |
Conclusion
The three equations of motion are used to solve problems involving constant acceleration in one-dimensional motion.
NEET Physics Practice Questions
Chapter: Uniformly Accelerated Motion (1-D)
NEET Question Types
- Direct MCQs (Single Correct Option)
- Statement Based Questions
- Assertion and Reason
- Match the Columns
- Diagram Based / Graphical Questions
PART 1: Direct MCQs (Single Correct Option)
Q1. A car starts from rest and accelerates uniformly at 4 m/s². Its velocity after 5 seconds will be:
A) 10 m/s
B) 20 m/s
C) 25 m/s
D) 40 m/s
u = 0
a = 4 m/s²
t = 5 s
v = u + at
v = 0 + 4 × 5
v = 20 m/s
Answer: B) 20 m/s
Q2. The SI unit of acceleration is:
A) m/s
B) m²/s
C) m/s²
D) km/h
Q3. A body moving with velocity 20 m/s is brought to rest in 5 seconds. The acceleration is:
A) +4 m/s²
B) -4 m/s²
C) +5 m/s²
D) -5 m/s²
a = (0-20)/5
a = -4 m/s²
Answer: B) -4 m/s²
Q4. The velocity-time graph for uniformly accelerated motion is:
A) Straight line
B) Circle
C) Parabola
D) Hyperbola
Q5. A particle starts from rest and travels 100 m in 5 seconds with uniform acceleration. Find acceleration.
A) 4 m/s²
B) 6 m/s²
C) 8 m/s²
D) 10 m/s²
100 = 0 + 1/2 × a × 25
a = 8 m/s²
Answer: C) 8 m/s²
PART 2: Statement Based Questions
Options:
A) Both statements true and II explains I
B) Both true but II does not explain I
C) I true, II false
D) I false, II true
Q6.
Statement I: Velocity-time graph for uniformly accelerated motion is a straight line.
Statement II: Acceleration is constant in uniformly accelerated motion.
Q7.
Statement I: Displacement can be zero even if distance travelled is not zero.
Statement II: Displacement depends only on initial and final position.
Q8.
Statement I: Acceleration due to gravity is constant near Earth's surface.
Statement II: Value of g is approximately 9.8 m/s².
PART 3: Assertion and Reason
Options:
A) Both true and R explains A
B) Both true but R does not explain A
C) A true, R false
D) A false, R true
Q9.
Assertion: A body moving with constant velocity has zero acceleration.
Reason: Acceleration is the rate of change of velocity.
Q10.
Assertion: Area under velocity-time graph gives displacement.
Reason: Velocity is displacement divided by time.
Q11.
Assertion: A body can have zero velocity and non-zero acceleration.
Reason: At highest point of upward motion, velocity is zero but acceleration acts downward.
PART 4: Match the Columns
| Column I | Column II |
|---|---|
| Velocity | m/s |
| Acceleration | m/s² |
| Displacement | m |
| Time | second |
PART 5: Diagram Based / Graphical Questions
Q14. The slope of velocity-time graph represents:
A) Distance
B) Velocity
C) Acceleration
D) Displacement
Q15. Area under velocity-time graph represents:
A) Acceleration
B) Displacement
C) Force
D) Momentum
Q16. Velocity-time graph:
v | | / | / | / |_____/________ t
The particle has:
A) Constant velocity
B) Constant acceleration
C) Zero acceleration
D) Variable acceleration
Hard Numerical Practice
Q17. A train moving at 72 km/h stops in 10 seconds. Find retardation.
Q18. A particle has initial velocity 5 m/s and acceleration 2 m/s². Find distance in 10 seconds.
NEET Formula Revision
s = ut + 1/2 at²
v² = u² + 2as
s = ((u+v)/2)t
NEET Tips
- Practice velocity-time graphs.
- Remember sign convention.
- Understand distance and displacement difference.
- Use correct equation according to given data.
- Practice free fall problems.
