Uniformly Accelerated Particle Model Worksheet Answers

Uniformly Accelerated Particle Model Worksheet Answers

The uniformly accelerated particle model is a fundamental concept in physics that describes the motion of an object under constant acceleration. This worksheet provides answers to common problems related to this topic.

Basic Equations

The following equations are essential for solving problems related to uniformly accelerated particles:

• Equation 1: v = u + at
• Equation 2: s = ut + (¹⁄₂)at^2
• Equation 3: v^2 = u^2 + 2as

where: v = final velocity u = initial velocity a = acceleration t = time s = displacement

Problem 1: Finding Final Velocity

A particle starts from rest and accelerates uniformly at 2 m/s^2 for 5 seconds. Find its final velocity.

Solution:

Using Equation 1: v = u + at u = 0 m/s (starts from rest) a = 2 m/s^2 t = 5 s

v = 0 + (2 m/s^2)(5 s) v = 10 m/s

Problem 2: Finding Displacement

A particle moves with an initial velocity of 4 m/s and accelerates uniformly at 3 m/s^2 for 8 seconds. Find its displacement.

Solution:

Using Equation 2: s = ut + (¹⁄₂)at^2 u = 4 m/s a = 3 m/s^2 t = 8 s

s = (4 m/s)(8 s) + (¹⁄₂)(3 m/s^2)(8 s)^2 s = 32 m + 96 m s = 128 m

Problem 3: Finding Acceleration

A particle moves with an initial velocity of 10 m/s and final velocity of 20 m/s in 4 seconds. Find its acceleration.

Solution:

Using Equation 1: v = u + at u = 10 m/s v = 20 m/s t = 4 s

20 m/s = 10 m/s + a(4 s) a = (20 m/s - 10 m/s) / 4 s a = 2.5 m/s^2

Problem 4: Finding Time

A particle moves with an initial velocity of 5 m/s and accelerates uniformly at 1.5 m/s^2. Find the time taken to reach a final velocity of 15 m/s.

Solution:

Using Equation 1: v = u + at u = 5 m/s v = 15 m/s a = 1.5 m/s^2

15 m/s = 5 m/s + (1.5 m/s^2)t t = (15 m/s - 5 m/s) / 1.5 m/s^2 t = 6.67 s

Notes

• 📝 Note: When solving problems, always check the units of the given values and ensure that they match the units of the equation.

• 📝 Note: Pay attention to the signs of the values. A positive acceleration indicates an increase in velocity, while a negative acceleration indicates a decrease in velocity.

Key Points

• The uniformly accelerated particle model describes the motion of an object under constant acceleration.
• The basic equations for this model are v = u + at, s = ut + (¹⁄₂)at^2, and v^2 = u^2 + 2as.
• These equations can be used to solve problems related to final velocity, displacement, acceleration, and time.

In summary, the uniformly accelerated particle model is a fundamental concept in physics that describes the motion of an object under constant acceleration. By understanding the basic equations and how to apply them, you can solve a variety of problems related to this topic.

Related Terms:

• Stacks of Kinematic graphs