A 3 kilogram block sits at rest on a frictionless surface. A force of 12 Newtons is applied to the block. How fast is the mass moving after 2 seconds?
To determine the speed of the mass after 2 seconds, we need to calculate the acceleration using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Given:
Mass (m) = 3 kg
Force (F) = 12 N
Rearranging the equation, we have:
Acceleration (a) = F / m
Plugging in the values, we get:
Acceleration (a) = 12 N / 3 kg
= 4 m/s²
Now, we can use the equation of motion to find the speed:
Speed = initial speed + (acceleration * time)
Since the block starts from rest, the initial speed is 0 m/s.
Plugging in the values, we get:
Speed = 0 m/s + (4 m/s² * 2 s)
= 0 m/s + 8 m/s
= 8 m/s
Therefore, the mass will be moving at a speed of 8 meters per second after 2 seconds.
To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is:
F = m * a
where F is the net force, m is the mass, and a is the acceleration.
In this case, the net force acting on the block is 12 Newtons, and the mass of the block is 3 kilograms. We want to find the acceleration of the block after 2 seconds.
Step 1: Calculate the acceleration.
We can rearrange Newton's second law equation to solve for acceleration:
a = F / m
Plugging in the values:
a = 12 N / 3 kg
a = 4 m/s²
Step 2: Calculate the final velocity.
We can use the kinematic equation to find the final velocity of an object after a certain time:
v = u + at
where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration, and t is the time.
Plugging in the values:
v = 0 + 4 m/s² * 2 s
v = 8 m/s
Therefore, the mass will be moving at a speed of 8 meters per second after 2 seconds.