A single constant force 18.1 N acts on a particle of mass 2.92 kg. The particle starts at rest at t=0. What is the instantaneous power delivered by the force at t=4.48s? Answer in units of W
a = F/m = 18.1/2.92 = 6.20 m/s^2.
V = Vo + a*t = 0 + 6.20*4.48 = 27.77 m/s
P=F*(d/t) = F*V = 18.1 * 27.77=502.6 J/s
= 502.6 Watts.
Well, when it comes to power, we can use the equation P = F * v, where P is power, F is force, and v is velocity. But in this case, we don't have the velocity directly given. However, we do know that the particle starts at rest, which means its initial velocity is zero.
So, at any given time t, we can find the velocity using the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time.
In this case, the force is constant (18.1 N), so the acceleration of the particle is a = F/m, where m is the mass.
Hence, a = 18.1 N / 2.92 kg.
Now, plug in the values to find the acceleration.
Then, use the acceleration to find the velocity at t = 4.48 s.
Finally, substitute the force and velocity into the formula P = F * v to find the instantaneous power.
And there you have it - the instantaneous power delivered by the force at t = 4.48 s. Now, don't forget to wear your power suit!
To find the instantaneous power delivered by a force, we can use the formula:
Power = Force × Velocity
But since we are given the mass of the particle instead of the velocity, we need to find the velocity first.
Using Newton's second law, we can find the acceleration of the particle:
Force = mass × acceleration
Rearranging the equation will give:
acceleration = Force / mass
Plugging in the given values:
acceleration = 18.1 N / 2.92 kg = 6.205 m/s²
Now, we can find the velocity of the particle at time t=4.48s using the kinematic equation:
velocity = initial velocity + acceleration × time
Since the particle starts at rest, the initial velocity is 0:
velocity = 0 + 6.205 m/s² × 4.48s = 27.78 m/s
Now that we have the velocity, we can find the instantaneous power:
Power = Force × Velocity
Plugging in the values:
Power = 18.1 N × 27.78 m/s = 502.418 W
Therefore, the instantaneous power delivered by the force at t=4.48s is 502.418 Watts.
To find the instantaneous power delivered by a force at a given time, we need to use the formula:
Power = Force * Velocity
In order to find the velocity at a given time, we can use Newton's second law of motion:
Force = Mass * Acceleration
We can rearrange this equation to get:
Acceleration = Force / Mass
Since the acceleration is constant, we can use the following equation to find the velocity at any time:
Velocity = Initial Velocity + (Acceleration * Time)
Given that the particle starts at rest, the initial velocity is 0. Therefore, we can simplify the equation to:
Velocity = Acceleration * Time
Now, let's calculate the acceleration:
Acceleration = Force / Mass
Acceleration = 18.1 N / 2.92 kg
Acceleration ≈ 6.21 m/s^2
Next, let's calculate the velocity at t=4.48s:
Velocity = Acceleration * Time
Velocity = 6.21 m/s^2 * 4.48 s
Velocity ≈ 27.82 m/s
Finally, let's calculate the instantaneous power at t=4.48s:
Power = Force * Velocity
Power = 18.1 N * 27.82 m/s
Power ≈ 503.16 W
Therefore, the instantaneous power delivered by the force at t=4.48s is approximately 503.16 W.