Question

A particle moves along the x-axis so that its velocity at time t its velocity is given by v(t) = 3 - 4.1cos(0.9t).

a) 3 - 4.1cos(0.9t)
b) 3 + 4.1cos(0.9t)
c) 3 - 4.1sin(0.9t)
d) 3 + 4.1sin(0.9t)

Answer 1

The particle crosses the origin at t = 2.0 seconds. The displacement of the particle between t = 3.0 s and t = 6.0 s is -6.0 meters. These answers address the motion of the particle and its change in position over time.

Step-by-step explanation:

The question asks about the motion of a particle under various conditions, including its velocity, acceleration, and position functions over time. Let's address each given situation:

27. Particle Crossing the Origin

To determine when the particle crosses the origin (x=0), set the position function x(t) = 4.0 - 2.0t to zero and solve for t:

4.0 - 2.0t = 0

2.0t = 4.0

t = 2.0 seconds

The particle crosses the origin at t = 2.0 seconds.

27. Displacement of the Particle

The displacement between two times is the difference in position. Calculate the positions at t = 3.0 s and t = 6.0 s, then subtract:

x(3.0 s) = 4.0 - 2.0(3.0) = -2.0 m

x(6.0 s) = 4.0 - 2.0(6.0) = -8.0 m

Displacement = x(6.0 s) - x(3.0 s) = -8.0 m - (-2.0 m) = -6.0 m

The displacement of the particle between t = 3.0 s and t = 6.0 s is -6.0 meters.