If a force of 15.0 N directed east acts on a stationary 5.00 kg mass, what are its acceleration, displacement, and velocity after 10.0 s?
a. T = ma,
a = F/m = 15 / 5 = 3m/s^2.
b. D = V0*t + 0.5a*t^2,
D = 0 + 1.5*10^2 = 150m.
Vf = Vo + at,
Vf = 0 + 3*10 = 30m/s.
Where does 0.5 comes from?
Well, there's an old saying in physics: "15 N of force makes the object go!" So, with a force of 15.0 N directed east, our 5.00 kg mass will definitely start moving. However, since we don't know the initial velocity, we can't use the simple kinematic equations to find the acceleration, displacement, and velocity after 10.0 s. We need more information, or we'd be taking shots in the dark like a blindfolded magician at a dartboard.
To find the acceleration, displacement, and velocity of the 5.00 kg mass, we can use Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, or F = ma.
Given:
Force (F) = 15.0 N
Mass (m) = 5.00 kg
Time (t) = 10.0 s
1. Find the acceleration (a):
Using Newton's second law, we can rearrange the formula to solve for acceleration:
a = F/m
Substituting the given values:
a = 15.0 N / 5.00 kg
a = 3.00 m/s^2
Therefore, the acceleration of the object is 3.00 m/s^2.
2. Find the displacement (s):
To find the displacement, we can use the equation of motion:
s = ut + (1/2)at^2
Since the object starts from rest (stationary), the initial velocity (u) is 0.
Substituting the values:
s = 0 + (1/2)(3.00 m/s^2)(10.0 s)^2
s = 0 + (1/2)(3.00 m/s^2)(100.0 s^2)
s = (1/2)(3.00 m/s^2)(100.0)
s = (1/2)(300.0)
s = 150.0 meters
Thus, the displacement of the object after 10.0 seconds is 150.0 meters.
3. Find the velocity (v):
To find the final velocity, we can use the equation:
v = u + at
Since the object starts from rest (stationary), the initial velocity (u) is 0.
Substituting the values:
v = 0 + (3.00 m/s^2)(10.0 s)
v = (3.00 m/s^2)(10.0 s)
v = 30.0 m/s
Therefore, the velocity of the object after 10.0 seconds is 30.0 m/s.