Particle Motion in Calculus
Explore particle motion concepts including position, velocity, and acceleration with this comprehensive worksheet for Grade 10 Calculus students.
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Particle Motion in Calculus
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Read each question carefully and provide detailed answers, showing all your work where applicable. Remember the relationships between position, velocity, and acceleration.
1. If the position of a particle is given by s(t) = t^3 - 6t^2 + 9t, what is the velocity of the particle at t = 2?
-3 m/s
0 m/s
3 m/s
6 m/s
2. When is the particle at rest if its velocity is v(t) = 3t^2 - 12t?
t = 0 only
t = 4 only
t = 0 and t = 4
Never at rest
1. The derivative of the position function gives the function.
2. If the velocity and acceleration have opposite signs, the particle is .
1. A particle moves along a horizontal line with position function s(t) = t^3 - 3t^2 - 9t + 5, where t is in seconds and s is in meters.
a) Find the velocity function v(t).
b) Find the acceleration function a(t).
c) When is the particle moving to the right?
d) When is the particle speeding up?
1. If the velocity of a particle is constant, then its acceleration is zero.
True
False
2. A particle is moving to the left if its velocity is negative.
True
False
Consider a particle whose position is given by s(t) = t^2 - 4t + 3.
1. Draw a number line to represent the particle's motion. Indicate the direction of motion and when the particle is at rest.