Particle Motion Calculus Worksheet
A Grade 12 Calculus worksheet focusing on particle motion, including displacement, velocity, acceleration, and interpreting motion graphs.
Includes
Standards
Topics
Particle Motion Calculus
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Read each question carefully and show all your work. Use appropriate units for your answers. Round to two decimal places where necessary.
1. A particle moves along the x-axis so that its position at time t (in seconds) is given by s(t) = t³ - 6t² + 9t, for t ≥ 0. Answer the following questions.
a) Find the velocity function v(t) and the acceleration function a(t).
b) Find the times when the particle is at rest.
c) Find the displacement of the particle from t = 0 to t = 5.
d) Find the total distance traveled by the particle from t = 0 to t = 5.
2. The graph below shows the velocity v(t) of a particle moving along a straight line for 0 ≤ t ≤ 8.
a) At what time interval(s) is the particle moving in the positive direction?
(0, 2)
(2, 4)
(4, 8)
(0, 8)
b) At what time does the particle change direction?
t = 2 and t = 4
t = 4
t = 0 and t = 8
t = 2
3. Indicate whether each statement is True or False.
a) If the velocity of a particle is constant, then its acceleration is zero.
True
False
b) If a particle's speed is increasing, its acceleration must be positive.
True
False
c) The total distance traveled by a particle is always greater than or equal to its displacement.
True
False
4. Complete the following sentences.
a) If the velocity and acceleration of a particle have opposite signs, the particle is .
b) The absolute value of velocity is called .
c) To find the total distance traveled, we must integrate the of the velocity function.
d) A particle is at rest when its is equal to zero.
5. A car is traveling on a straight road. Its acceleration is given by a(t) = 6t - 12 ft/s². At t = 0, the car's velocity is 9 ft/s and its position is 5 ft.
a) Find the velocity function v(t).
b) Find the position function s(t).
c) When is the car moving backward?