Accelerating car, kinematics problem

In summary: The car's mass is 2.3 x 10^3 kg, initial velocity is 0 m/s, final velocity is +17 m/s, and time is 21 seconds. Air resistance is constant at -500 N. We are looking for the average power developed by the engine and the instantaneous power developed at t = 15 s. In summary, we are given the necessary information to calculate power, which is the work done per unit time. By using the equation Power = Work / time, we can find the average power developed by the engine and the instantaneous power developed at t = 15 s by using the known values for mass, initial and final velocity, and time.
  • #1
Jessicaelleig
12
0
A 2.3 103 kg car starts from rest and accelerates along a horizontal roadway to +17 m/s in 21 s. Assume that air resistance remains constant at -500 N during this time. Find
(a) the average power developed by the engine and

(b) the instantaneous power developed at t = 15 s.

I am really confused about this. If you can help, I would appreciate it. Thanks!
 
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  • #2


Jessicaelleig said:
A 2.3 103 kg car starts from rest and accelerates along a horizontal roadway to +17 m/s in 21 s. Assume that air resistance remains constant at -500 N during this time. Find
(a) the average power developed by the engine and

(b) the instantaneous power developed at t = 15 s.

I am really confused about this. If you can help, I would appreciate it. Thanks!

I find a good place to start on any problem is to list the knowns and unknowns, then find equations that deal with those properties/units.

For instance, here you are given :
mass
initial velocity
final velocity
time
a force acting on the system

and you are looking for:
power

Keep in mind, power will have units in terms of Watts (or kW)
Power = Work / time
Work = Force * distance
Force = mass * acceleration


See if you can get started with that.
 
  • #3


Sure, I can help you with this problem. I understand that kinematics is the study of motion, and we can use equations to analyze the motion of objects. In this scenario, we are dealing with an accelerating car, which means that its velocity is changing over time. The car has a mass of 2.3 x 10^3 kg and starts from rest, meaning its initial velocity is 0 m/s. After 21 seconds, its final velocity is +17 m/s.

To solve this problem, we can use the equation for average acceleration, which is a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time taken. Plugging in the given values, we get:

a = (+17 m/s - 0 m/s) / 21 s = 0.81 m/s^2

This means that the car's acceleration is 0.81 m/s^2. Now, we also need to take into account the air resistance, which is a force acting in the opposite direction of motion. We can use Newton's second law, F = ma, to calculate the net force acting on the car.

F = (2.3 x 10^3 kg)(0.81 m/s^2) - 500 N = 1863 N - 500 N = 1363 N

This net force is what is causing the car to accelerate. Now, to find the average power developed by the engine, we can use the equation for power, P = Fv, where F is the net force and v is the average velocity. We know the net force, but we need to find the average velocity. We can use the equation for average velocity, v = (vf + vi)/2, where vf is the final velocity and vi is the initial velocity.

v = (+17 m/s + 0 m/s)/2 = 8.5 m/s

Now, we can plug in the values to find the average power:

P = (1363 N)(8.5 m/s) = 11,579.5 W = 11.6 kW

This is the average power developed by the engine to accelerate the car.

For part (b) of the problem, we need to find the instantaneous power developed at t = 15 s. To do this, we can use the equation for instantaneous power,
 

1. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is measured in meters per second squared (m/s^2).

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What is the difference between acceleration and velocity?

Velocity is the rate of change in an object's displacement over time, while acceleration is the rate of change in an object's velocity over time. In other words, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how quickly the object's velocity is changing.

4. How does acceleration affect the motion of a car?

Acceleration affects the motion of a car by increasing or decreasing its speed. A positive acceleration will cause the car to speed up, while a negative acceleration (also known as deceleration) will cause the car to slow down. The direction of the acceleration will also affect the direction in which the car is moving.

5. How can acceleration be used to solve kinematics problems?

Acceleration can be used in kinematics problems to calculate the final velocity, initial velocity, or time taken for an object to reach a certain position. It can also be used to determine the displacement of an object during a given time period. By understanding the relationship between acceleration, velocity, and time, we can accurately describe and predict the motion of an object.

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