Particle Motion Worksheet
Explore particle motion concepts including position, velocity, and acceleration with this comprehensive worksheet for Grade 9 Calculus students.
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Particle Motion Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
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 = 3 seconds.
2. If the velocity of a particle is positive, the particle is moving to the .
3. If the acceleration of a particle is negative, the velocity of the particle is .
4. When the velocity and acceleration have opposite signs, the particle is .
5. A particle's position is given by s(t) = t² - 4t + 3. At what time(s) is the particle at rest?
t = 0
t = 1
t = 2
t = 3
6. If a particle is slowing down, its velocity and acceleration must have the same sign.
True
False
7. A particle moves along a number line. Its position at time t is given by x(t) = t³ - 3t².
a) Find the intervals where the particle is moving to the right.
b) Find the intervals where the particle is moving to the left.
c) Find the total distance traveled by the particle from t = 0 to t = 4.
8. Plot the critical points of velocity for the function s(t) = t² - 6t + 5 on the number line below.
9. The graph below shows the velocity v(t) of a particle moving along a straight line.
a) On what interval(s) is the particle moving forward?
b) On what interval(s) is the particle moving backward?
c) On what interval(s) is the particle speeding up?