Download 1. Two particles move along the x-axis. For 0 ≤ ≤ 6, the position of

1. Two particles move along the x-axis. For 0 ≤ 𝑡 ≤ 6, the position of particle P at time t is
𝜋
given by 𝑝(𝑡) = 2 cos( 4 𝑡), while the position of particle R at time t is given by
𝑟(𝑡) = 𝑡 3 − 6𝑡 2 + 9𝑡 + 3.
a) For 0 ≤ 𝑡 ≤ 6, find all times, t, during which the particle R is moving to the right.
b) For 0 ≤ 𝑡 ≤ 6, find all times, t, during which R and P are moving in opposite directions.
2.
1. A particle moves along the x-axis so that its velocity, v, at time 𝑡 ≥ 0 is given by: 𝑣(𝑡) = sin(𝑡 2 ).
The graph of v(t) is shown above. The position of the particle at time t is 𝑥(𝑡), and at time t = 0,
the position of the particle is 5 (x(0) = 5).
a)
Find the acceleration of the particle at time t = 3.
b) At what times, t, is the velocity, v(t) = 0.
c)
Find the total distance traveled by the particle from time t = 0 to t = 3.
d) Find the displacement of the particle from t=0 to t = 3.
BONUS: Find the position of the particle at time t = 3