A car of mass 1200kg starts from rest, accelerates uniformly to a speed of 4.0 meters per second in 2.0 seconds and continues moving at this constant speed in a horizontal straight line for an additional 10 seconds. the brakes are then applied and the car is brought to rest in 4.0 seconds. A constant resistance force of 500N is acting on the car during its entire motion.
a) Calculate the force accelerating the car in the first 2.0 seconds of the motion
b) Calculate the average power developed by the engine in the first 2.0 seconds of the motion
c) calculate the force pushing the car forward in the next 10 seconds
d) Calculate the power developed by the engine in those 10 seconds
e) Calculate the braking force in the last 4.0 seconds of the motion
f) Describe the energy transformations that have taken place in the 16 seconds of the motion of this car
a. F = m*a.
a = (V-Vo)/t = (4-0)/2 = 2 m/s^2.
F = 1200*2 = 2400 N.
b. d = 0.5a*t2.
d = 0.5*2*2^2 = 4 m.
P = F*d/t = 2400 * 4/2 = 4800 Joules/s.
1. A car starts from rest and accelerates at 3 m/s2 for 5 seconds and then continues with constant velocity. Calculate the distance covered in 15 seconds since it starts from rest.
a) To calculate the force accelerating the car in the first 2.0 seconds of motion, we can use Newton's second law of motion:
F = ma
Given mass (m) = 1200 kg and time (t) = 2.0 seconds, we can rearrange the equation to solve for force (F):
F = ma = (1200 kg)(4.0 m/s^2) = 4800 N
Therefore, the force accelerating the car in the first 2.0 seconds of motion is 4800 N.
b) To calculate the average power developed by the engine in the first 2.0 seconds of motion, we can use the formula:
Power = work / time
The work done on an object is given by:
Work = force x distance
In this case, the force (F) is 4800 N and the distance is not given. However, we can use the formula for uniform acceleration to find the distance:
distance = (1/2)at^2
Substituting the values, we have:
distance = (1/2)(4.0 m/s^2)(2.0 s)^2 = 8.0 m
Now, we can calculate the work:
Work = force x distance = (4800 N)(8.0 m) = 38400 J
Finally, we can calculate the average power:
Power = work / time = 38400 J / 2.0 s = 19200 W
Therefore, the average power developed by the engine in the first 2.0 seconds of motion is 19200 W.
c) In the next 10 seconds, the car continues moving at a constant speed of 4.0 m/s. Since it is moving at a constant speed, the net force acting on the car must be zero. The constant resistance force of 500 N provides the force pushing the car forward during this time.
Therefore, the force pushing the car forward in the next 10 seconds is 500 N.
d) To calculate the power developed by the engine in the next 10 seconds, we can use the formula:
Power = work / time
As mentioned earlier, since the net force is zero and no work is being done, the power developed by the engine in the next 10 seconds is also zero.
Therefore, the power developed by the engine in the next 10 seconds is zero.
e) In the last 4.0 seconds of motion, the brakes are applied to bring the car to rest. The car experiences a constant braking force until it comes to a stop. We need to calculate the braking force.
Using Newton's second law of motion as before:
F = ma
Given mass (m) = 1200 kg and time (t) = 4.0 seconds, we can rearrange the equation to solve for the braking force (F):
F = ma = (1200 kg)(-4.0 m/s^2) = -4800 N
The negative sign indicates that the braking force acts in the opposite direction to the motion of the car.
Therefore, the braking force in the last 4.0 seconds of motion is -4800 N.
f) The energy transformations that have taken place in the 16 seconds of the motion of this car are as follows:
1. In the first 2.0 seconds, the engine does work on the car to give it kinetic energy. The chemical energy stored in the fuel is converted into mechanical energy in the form of the engine's power.
2. In the following 10 seconds, the car continues moving at a constant speed. No energy transformations occur since the net force on the car is zero.
3. In the last 4.0 seconds, the brakes are applied, and the car comes to rest. The kinetic energy of the car is converted into other forms of energy like thermal energy due to the braking force and sound energy due to any noise generated during braking.
Overall, the initial chemical energy in the fuel is transformed into mechanical energy, and then into heat and sound energy during the braking process.
a) To calculate the force accelerating the car in the first 2.0 seconds, we can use Newton's second law of motion:
Force = Mass * Acceleration
Given:
Mass (m) = 1200 kg
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
Using the formula for acceleration, we can calculate it as follows:
Acceleration = (4.0 m/s - 0) / 2.0 s
Once we have the acceleration, we can calculate the force using Newton's second law:
Force = Mass * Acceleration
Force = 1200 kg * (4.0 m/s - 0) / 2.0 s
b) To calculate the average power developed by the engine in the first 2.0 seconds, we can use the formula:
Power = Force * Velocity
Given:
Force (from part a) = ?
Velocity = (Final Velocity + Initial Velocity) / 2
Using the formula for average velocity, we can calculate it as follows:
Velocity = (4.0 m/s + 0) / 2
Once we have the force and velocity, we can calculate the power using the formula:
Power = Force * Velocity
Power = ? * ((4.0 m/s + 0) / 2)
c) To calculate the force pushing the car forward in the next 10 seconds, we need to consider the constant resistance force acting on the car. The net force is given by:
Net Force = Force Pushing the Car Forward - Resistance Force
Given:
Resistance Force = 500 N
To calculate the force pushing the car forward, we need the net force. Since the car is moving at a constant speed, the net force is zero:
Net Force = 0
Therefore,
Force Pushing the Car Forward = Resistance Force
Force Pushing the Car Forward = 500 N
d) To calculate the power developed by the engine in those 10 seconds, we can use the same formula as in part b:
Power = Force * Velocity
Given:
Force Pushing the Car Forward (from part c) = ?
Velocity = (Final Velocity + Initial Velocity) / 2
Using the formula for average velocity, we can calculate it as follows:
Velocity = (4.0 m/s + 4.0 m/s) / 2
Once we have the force and velocity, we can calculate the power using the formula:
Power = Force * Velocity
Power = ? * ((4.0 m/s + 4.0 m/s) / 2)
e) To calculate the braking force in the last 4.0 seconds of motion, we need to consider the deceleration of the car. Deceleration (a) can be calculated as:
Deceleration = -(Final Velocity - Initial Velocity) / Time
Using the given values, we can calculate deceleration as follows:
Deceleration = -(0 - 4.0 m/s) / 4.0 s
Once we have the deceleration, we can calculate the braking force using Newton's second law:
Braking Force = Mass * Deceleration
Braking Force = 1200 kg * (-(0 - 4.0 m/s) / 4.0 s)
f) In the 16 seconds of motion, several energy transformations take place. Initially, the car is at rest, and as it accelerates, the energy is transformed from potential energy (stored energy) to kinetic energy (energy of motion). This transformation occurs during the first 2.0 seconds.
During the next 10 seconds, as the car moves at a constant speed, the engine continues to provide power to overcome the resistance force. The energy from the engine is transformed into kinetic energy, which keeps the car moving at a constant speed.
During the last 4.0 seconds, the brakes are applied to bring the car to rest. The kinetic energy of the car is transformed into other forms of energy, mainly heat and sound, due to the friction between the brakes and the car's wheels.
Overall, the main energy transformations in this motion are from potential energy to kinetic energy, and then from kinetic energy to other forms of energy (heat and sound) during braking.