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Class 11 Physics Motion in a Plane Example 3.5 Solution

Dr.Sanjaykumar pawar
Educational diagram explaining motion in a plane with velocity and acceleration vectors for Class 11 physics students.
Step-by-step solution of particle motion in x-y plane using velocity and acceleration vectors.

Example 3.5 Notes

Example 3.5 — Easy Beginner Notes

A particle starts from the origin at t = 0 with velocity:

v = 5i m/s

Constant acceleration is:

a = (3i + 2j) m/s²
  • Acceleration in x-direction = 3 m/s²
  • Acceleration in y-direction = 2 m/s²

Step 1: Position Formula

r = r₀ + v₀t + ½at²

Since particle starts from origin:

r₀ = 0

So,

r = v₀t + ½at²

Step 2: Put Given Values

v₀ = 5i
a = 3i + 2j

Substitute in position formula:

r = 5it + ½(3i + 2j)t²

Step 3: Simplify

r = 5ti + 1.5t²i + 1.0t²j
r = (5t + 1.5t²)i + (1.0t²)j

Step 4: Write x and y Coordinates

x = 5t + 1.5t²
y = 1.0t²

Part (a): Find y-coordinate when x = 84 m

Given:

x = 84

Put in x-equation:

5t + 1.5t² = 84
Solve the equation:

1.5t² + 5t - 84 = 0

t = 6 s

Step 5: Find y-coordinate

y = 1.0t²

Put t = 6:

y = 1.0 × (6)²
y = 36 m
Answer (a): y = 36 m

Part (b): Find Speed at t = 6 s

Step 6: Velocity Formula

v = v₀ + at

Substitute values:

v = 5i + (3i + 2j)t

Put t = 6 s:

v = 5i + (3×6)i + (2×6)j
v = 23i + 12j
  • x-component of velocity = 23 m/s
  • y-component of velocity = 12 m/s

Step 7: Find Speed

Speed = √(vx² + vy²)
Speed = √(23² + 12²)
Speed = √(529 + 144)
Speed = √673
Speed ≈ 26 m/s
Answer (b): Speed = 26 m/s

Quick Beginner Understanding

  • i represents x-direction
  • j represents y-direction
  • Position formula gives location of particle
  • Velocity formula gives motion speed and direction
  • Speed is magnitude of velocity vector
  • x and y motions are solved separately

Internal Links
Introduction to Motion in a Plane
Vector Basics for Beginners
Velocity and Acceleration Explained
Kinematics Formulas with Examples
Solved Numerical Problems for Class 11 Physics
Projectile Motion Notes
NCERT Physics Chapter 3 Solutions
Scalar and Vector Quantities
Motion Along Straight Line Notes
Physics Formula Sheet for Students
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