Particle Motion in Calculus
This worksheet covers fundamental concepts of particle motion using calculus, including position, velocity, acceleration, and displacement.
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Particle Motion in Calculus
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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