The kinetic energy of a moving object is related to its mass and velocity by the formula Ek=1/2mv^2 , where Ek is the kinetic energy in joules, m is the mass of the object in kilograms, and v is the object’s velocity in metres per second. What are the possible velocities for a 3 kg object with a kinetic energy of less than 600 J? (Negative velocities are acceptable and represent the opposite direction of a positive velocity.)
1/2 * 3 * v^2 < 600
v^2 < 400
now finish it off
To find the possible velocities for a 3 kg object with a kinetic energy of less than 600 J, we can rearrange the formula:
Ek = 1/2mv^2
Using algebraic manipulation, we isolate the velocity (v):
v^2 = 2Ek / m
v = √(2Ek / m)
Now we can substitute the given values:
m = 3 kg
Ek < 600 J
v = √(2 * 600 J / 3 kg)
v = √(1200 J / 3 kg)
v = √(400 J / kg)
To calculate the square root, we can simplify the terms:
v = √(400) m/s
v = 20 m/s
Therefore, the possible velocities for a 3 kg object with a kinetic energy of less than 600 J are any velocity less than +20 m/s or greater than -20 m/s.
To find the possible velocities for a 3 kg object with a kinetic energy of less than 600 J, we can rearrange the formula for kinetic energy to solve for velocity.
The formula for kinetic energy is given as Ek = 1/2mv^2.
Rearranging the formula, we get: v^2 = (2Ek) / m.
Substituting the given values, we have: v^2 = (2 * 600 J) / 3 kg.
Simplifying further, we get: v^2 = 400 m^2/s^2.
To find the possible velocities, we need to take the square root of both sides of the equation.
Taking the square root, we have: v = ±√(400) = ±20 m/s.
Therefore, the possible velocities for a 3 kg object with a kinetic energy of less than 600 J are +20 m/s and -20 m/s. The positive velocity represents the object moving in the forward direction, while the negative velocity represents the object moving in the opposite (or backward) direction.