a resultant force of 5N acts for 5s on a mass of 5kg initially at rest. find the velocity acquired and distance mode
To find the velocity acquired and the distance moved by the mass, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the force acting on it divided by its mass:
Acceleration (a) = Force (F) / Mass (m)
In this case, the force acting on the object is 5 N and its mass is 5 kg.
Acceleration = 5 N / 5 kg
Acceleration = 1 m/s²
Next, we can use the equation of motion to find the velocity acquired:
Final Velocity (v) = Initial Velocity (u) + (Acceleration × Time)
Since the object is initially at rest, the initial velocity (u) is 0:
Final Velocity (v) = 0 + (1 m/s² × 5 s)
Final Velocity (v) = 5 m/s
Therefore, the velocity acquired by the mass under the given conditions is 5 m/s.
To find the distance moved (s), we can use another equation of motion:
Distance (s) = Initial Velocity (u) × Time + (1/2) × Acceleration × Time²
Since the initial velocity (u) is 0, the equation simplifies to:
Distance (s) = (1/2) × Acceleration × Time²
Distance (s) = (1/2) × 1 m/s² × (5 s)²
Distance (s) = (1/2) × 1 m/s² × 25 s²
Distance (s) = 0.5 m/s² × 25 s²
Distance (s) = 12.5 m
Therefore, the distance moved by the mass under the given conditions is 12.5 meters.
To find the velocity acquired and distance moved by the object, we can use the equations of motion. In this case, we will use the equation:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (which is 0 since the object is initially at rest)
- a is the acceleration (which we can calculate using Newton's second law, F = ma)
- t is the time
1. Calculate the acceleration:
Since we know the force (5N) and mass (5kg), we can use Newton's second law: F = ma
Rearranging the equation, we can find the acceleration:
a = F/m = 5N / 5kg = 1 m/s²
2. Calculate the final velocity:
Using the equation v = u + at, substitute the values:
v = 0 + (1 m/s²) * 5s = 5 m/s
3. Calculate the distance moved:
To find the distance moved, we can use the equation:
s = ut + (1/2)at²
Since the initial velocity (u) is 0, the equation simplifies to:
s = (1/2)at²
Substituting the values:
s = (1/2) * (1 m/s²) * (5s)² = (1/2) * (1 m/s²) * 25s² = 12.5 meters
Therefore, the velocity acquired is 5 m/s, and the distance moved is 12.5 meters.
Force * time = change of momentum (impulse)
5 N * 5 s = 25 = 5 * (v-0)
so v = 5 meters/second
The force is constant so the rate of change of velocity is constant and you can use the average velocity which is 5/2= 2.5 m/s
2.5 * 5 = 12.5 meters
or,
F = ma, so a = 1 m/s^2
v = at = 5*1 = 5 m/s
s = 1/2 at^2 = 1/2 * 1 * 5^2 = 12.5 m