An object with a mass of 0.75 kg is projected over a horizontal surface with a speed of 2.5 m/s. It then comes to rest after 3.0 s.
c) How far did the object move before coming to rest?
The object moved 7.5 m before coming to rest.
To determine how far the object moved before coming to rest, we can use the formulas of motion. Specifically, we can use the formula for calculating distance traveled during constant acceleration:
d = ut + (1/2)at^2
where:
- d is the distance traveled
- u is the initial velocity
- t is the time elapsed
- a is the acceleration
In this case, the object is projected horizontally, so there is no vertical acceleration. Therefore, the only force acting on the object is a horizontal force due to friction, which causes it to decelerate until it comes to rest. This horizontal force can be expressed as:
Fr = ma
where:
- m is the mass of the object
- a is the acceleration due to friction
Since the object comes to rest, its final velocity is 0. We can use this fact to determine the acceleration due to friction:
v = u + at
0 = 2.5 - a * 3
Rearranging the equation, we find:
a = 2.5 / 3
Substituting the value of acceleration into the formula for distance traveled, we have:
d = 2.5 * 3 + (1/2) * (2.5/3) * 3^2
Simplifying the equation:
d = 7.5 + (1/2) * (2.5/3) * 9
d = 7.5 + (5/6) * 9
d = 7.5 + 7.5
d = 15 meters
Therefore, the object moved a distance of 15 meters before coming to rest.
To find the distance the object moved before coming to rest, we can use the equation:
d = vt
where d is the distance, v is the initial velocity, and t is the time.
Given:
Mass of the object (m) = 0.75 kg
Initial velocity (v) = 2.5 m/s
Time taken to come to rest (t) = 3.0 s
Substituting the given values into the equation:
d = (2.5 m/s) * (3.0 s)
Calculating the result:
d = 7.5 m
Therefore, the object moved a distance of 7.5 meters before coming to rest.