Particle Motion in Calculus
This worksheet covers fundamental concepts of particle motion using calculus, including position, velocity, acceleration, and displacement.
Includes
Standards
Topics
Particle Motion in Calculus
Name:
Date:
Score:
Read each question carefully and show all your work. Use proper calculus notation where appropriate.
1. The position of a particle moving along the x-axis is given by the function s(t) = t³ - 6t² + 9t - 2, where t is in seconds and s(t) is in meters.
a) Find the velocity function v(t) of the particle.
b) Find the acceleration function a(t) of the particle.
c) Find the velocity of the particle at t = 2 seconds.
d) Find the acceleration of the particle at t = 2 seconds.
2. For the particle in question 1, when is the particle moving to the right?
t < 1 or t > 3
1 < t < 3
t = 1 and t = 3
Never
3. The velocity of a particle is given by v(t) = 2t - 4 m/s. The particle starts at position s(0) = 3 meters.
a) Find the position function s(t) of the particle. s(t) =
b) Find the displacement of the particle from t = 0 to t = 3 seconds. Displacement =
c) Find the total distance traveled by the particle from t = 0 to t = 3 seconds. Total Distance =
4. A particle moves along a straight line with velocity v(t) = t² - 5t + 6. Determine the time intervals when the particle is speeding up and slowing down.
5. True or False: If the velocity of a particle is zero, then its acceleration must also be zero.
True
False
Related Worksheets
Introduction to Differential Equations
This worksheet introduces fundamental concepts and methods for solving basic differential equations suitable for Grade 11 students.
Extrema in Calculus
Explore finding local and absolute extrema of functions using derivatives in this Grade 11 Calculus worksheet.
Squeeze Theorem Worksheet
A Grade 11 Math worksheet focusing on understanding and applying the Squeeze Theorem to evaluate limits, with various question types.
AP Calculus Foundations Worksheet
This worksheet covers fundamental concepts in AP Calculus, including limits, derivatives, and their applications, suitable for Grade 11 students.
Limits and Continuity Worksheet
Grade 11 Calculus worksheet covering limits, continuity, and related concepts with various question types.
Limits at Infinity Worksheet
Explore the behavior of functions as input values approach positive and negative infinity with this Grade 11 Calculus worksheet.
Intermediate Value Theorem Worksheet
Explore the Intermediate Value Theorem with this worksheet for Grade 11 Calculus students, covering its definition, application, and conditions.
Product Rule Practice Worksheet
Practice applying the product rule for differentiation in various calculus problems.