Question

The velocities of a 3.0-kg object at t=6.0s and t=8.0s are (3.0i − 6.0ʲ + 4.0ᵏ) m/s and (−2.0i + 4.0ᵏ) m/s, respectively. If the object is moving at constant acceleration, what is the force acting on it?

a) (−1 Ni + 3 Nʲ − 2 Nᵏ)
b) (1 Ni + 3 Nʲ − 2 Nᵏ)
c) (−1 Ni − 3 Nʲ + 2 Nᵏ)
d) (1 Ni − 3 Nʲ + 2 Nᵏ)

Answer 1

To find the force acting on the object, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. Given the velocities at two different times, we can find the acceleration of the object by taking the difference of the velocities and dividing by the time interval. Now that we have the acceleration, we can use Newton's second law to calculate the force.

Step-by-step explanation:

To find the force acting on the object, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.

Given the velocities at two different times, we can find the acceleration of the object by taking the difference of the velocities and dividing by the time interval:

a = (vf - vi) / t

Substituting the values, we find:
a = ((-2.0i + 4.0k) - (3.0i - 6.0ʲ + 4.0ᵏ)) / (8.0s - 6.0s) = (-5.0i + 6.0ʲ) m/s²

Now that we have the acceleration, we can use Newton's second law to calculate the force:
F = m * a = (3.0kg) * (-5.0i + 6.0ʲ) m/s² = -15.0i + 18.0ʲ N