Name _______________________________
4.5 Kinematics Practice
1. A particle moves along a straight line with its postion given by 𝑠 = 𝑡 3 − 9𝑡 2 + 24𝑡 − 16.
a. At what times does it change direction?
b. Find the total distance traveled by the particle after 5 seconds.
2. A particle is moving along an s-axis, where s is in feet. During the first 5 seconds of motion,
the position of the particle is given by
𝑠 = 10 − (3 − 𝑡)2 , 0 ≤ 𝑡 ≤ 5
Use the position function to complete each part.
Before the particle changes direction, it moves a total of _______ feet in the __________
(positive/negative) direction. After the particle changes direction, it travels a distance of
_____ feet during the remainder of the 5-second period.
3. A particle moves along a straight line so that at time t its position is given by
𝑓(𝑡) = sin(𝜋𝑡 2 ) for -1 ≤ t ≤ 1. [hint: your answer can include negative, only answers within
this interval are accepted]
a. Find the velocity function.
b. For what values of t does the particle change direction?
c. When is the particle moving to the left?
4. A particle moves along a straight line so that at time t its position is given by
𝑠(𝑡) = 𝑡 3 − 6𝑡 2 + 9𝑡 + 11. t > 0
a. What is the velocity of the particle at t = 0?
b. During what time intervals is the particle moving to the left?
c. What is the total distance traveled by the particle from t = 0 to t = 2?
5. The displacement s metres at time t seconds is given by
s = 5 cos 3t + t2 + 10, for t ≤ 0.
(a)
Write down the minimum value of s.
(b)
Find the acceleration, a, at time t.
(c)
Find the value of t when the maximum value of a first occurs.