Question

What is the particle's position at t =3.0s ? express your answer to three significant figures and include the appropriate units?

Answer 1

The position of a particle moving along the x-axis can be determined using the equation x(t) = 4.0 + 2.0t. The particle does not cross the origin and the displacement between t = 3.0 s and t = 6.0 s is 16.0 meters.

Step-by-step explanation:

The position of a particle moving along the x-axis is given by x(t) = 4.0 + 2.0t m.

(a) To find when the particle crosses the origin, we set x(t) = 0 and solve for t:
4.0 + 2.0t = 0
t = -2.0 seconds

Since time cannot be negative, the particle does not cross the origin.

(b) The displacement of the particle between t = 3.0 s and t = 6.0 s can be found by subtracting the position x(t=3.0s) from x(t=6.0s):
x(t=6.0s) - x(t=3.0s) = (4.0 + 2.0 * 6.0) - (4.0 + 2.0 * 3.0) = 16.0 meters

Answer 2

The only given information is the time in 3 seconds. We are asked to find the position, or the distance traveled. The working equation to be used here is:

x = v₀t + 1/2 at²
where
x is the distance
v₀ is the initial velocity
a is the acceleration

In order to solve this, let's assume the object is free falling. So v₀ = 0 and a = 9.81 m/s².

x = 0 + 1/2 (9.81)(3)²
x = 44.145 meters