Consider a 4.6 kilogram object moves from the origin always to the right (call that x-axis). Its speed increases uniformly (means constant acceleration) from zero to 0.667 metres/sec.
1.Describe how its velocity changes: initial, final and whether it changes uniformly.
2.The object takes 2.8 seconds to reach to that final speed. Describe its acceleration vector.
3.Write an equation for its speed in terms of time.
4.Find an equation for its kinetic energy as a function of time.
5.Use Newton's second law: F=(mass)a to calculate the total force acting on the object. Remember that force and acceleration are vectors.
1. The initial velocity of the object is zero since it starts from rest. The final velocity is 0.667 m/s, as stated in the question. The velocity changes uniformly because the acceleration is constant.
2. To find the acceleration vector, we can use the formula:
acceleration = (change in velocity) / (time taken)
Since the initial velocity is zero, the change in velocity is equal to the final velocity. Therefore, the acceleration vector is:
acceleration = (0.667 m/s - 0 m/s) / 2.8 s
acceleration = 0.667 m/s / 2.8 s
acceleration ≈ 0.238 m/s² to the right (since the object is moving to the right)
3. To find the equation for the speed of the object in terms of time, we can use the equation of motion:
final velocity = initial velocity + (acceleration * time)
Given that the initial velocity is zero and the acceleration is constant, the equation becomes:
speed = acceleration * time
Substituting the values, we have:
speed = 0.238 m/s² * time
4. The kinetic energy of an object is given by the equation:
kinetic energy = 0.5 * mass * velocity²
In this case, the velocity will be changing with time. Therefore, we substitute the equation for speed in terms of time into the equation for kinetic energy:
kinetic energy = 0.5 * mass * (acceleration * time)²
kinetic energy = 0.5 * mass * acceleration² * time²
5. We can use Newton's second law of motion, F = ma, to calculate the total force acting on the object. Since force and acceleration are vector quantities, we need to consider their magnitudes and directions.
Given that the mass of the object is 4.6 kg and the acceleration is 0.238 m/s² to the right, the total force acting on the object is:
force = mass * acceleration
force = 4.6 kg * 0.238 m/s²
force ≈ 1.095 N to the right (since the acceleration is to the right)