Class 11 Physics Motion in a Plane Example 3.5 Solution

Dr.Sanjaykumar pawar

Step-by-step solution of particle motion in x-y plane using velocity and acceleration vectors.

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