A car, starting from rest, accelerates in the positive x direction. It has a mass of 1.10 x 103 kg and maintains an acceleration of 4.6 m/s^2 for 5 s. Assume that a single horizontal force accelerates the vehicle. Determine the power generated by this force.
F = M*a = 1100 * 4.6 = 5060 N.
d = 0.5a*t^2 = 0.5*4.6*5^2 = 57.5 m.
P = F*d/t = 5060 * 57.5/5 = 58,190 J./s
= 58,190 W.
To determine the power generated by the force, we need to find the work done by the force and divide it by the time taken.
Firstly, let's calculate the work done by the force. The work done by a force is given by the formula:
Work = Force x Displacement x cos(theta)
Where:
Force is the magnitude of the force in the direction of displacement.
Displacement is the distance traveled by the car.
Theta is the angle between the direction of the force and the direction of displacement.
In this case, the car is moving in a straight line in the positive x direction, so the angle theta is 0 degrees, and cos(theta) is 1.
Since the car starts from rest, we can find the displacement using the formula:
Displacement = (1/2) x acceleration x time^2
Substituting the given values:
Acceleration = 4.6 m/s^2
Time = 5 s
Displacement = (1/2) x 4.6 m/s^2 x (5 s)^2 = 57.5 m
Next, let's calculate the force using Newton's second law: F = mass x acceleration.
Mass = 1.10 x 10^3 kg
Acceleration = 4.6 m/s^2
Force = 1.10 x 10^3 kg x 4.6 m/s^2 = 5060 N
Now, we can calculate the work done:
Work = Force x Displacement x cos(theta) = 5060 N x 57.5 m x 1 = 290,650 J (Joules)
Finally, we can calculate the power generated by the force:
Power = Work / Time
Power = 290,650 J / 5 s ā 58,130 W (Watts)
Therefore, the power generated by the force is approximately 58,130 Watts.
To determine the power generated by the force, we can use the formula:
Power = Force x Velocity
First, we need to find the force acting on the car. Using Newton's second law of motion:
Force = mass x acceleration
Given that the mass of the car is 1.10 x 10^3 kg and the acceleration is 4.6 m/s^2, we can calculate the force:
Force = (1.10 x 10^3 kg) x (4.6 m/s^2)
= 5060 N
Now, we need to find the velocity of the car after 5 seconds. Since the car started from rest and maintained a constant acceleration of 4.6 m/s^2 for 5 seconds, we can use the kinematic equation:
V = Vā + (a x t)
Where:
Vā is the initial velocity (which is zero in this case)
a is the acceleration (4.6 m/s^2)
t is the time (5 s)
V = 0 + (4.6 m/s^2 x 5 s)
= 23 m/s
Now, we can calculate the power generated by the force:
Power = Force x Velocity
= (5060 N) x (23 m/s)
= 116,380 watts or 116.38 kilowatts
So, the power generated by the force is 116.38 kilowatts.