Instantaneous Velocity Car Problem

In summary, the conversation involves calculating the average velocity of a car traveling along a straight road with a given displacement equation. The average velocity can be found by dividing the total distance traveled by the time interval. The question also involves finding the time when the car is at rest, which can be determined using another equation related to the displacement function and the quadratic formula may be used to solve for t.
  • #1
mopar969
201
0
A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t)= bt^2 -ct^3, where b = 2.40m/s^2 and c = 0.120 m/s^3. How do you calculate the average velocity of the car for the time interval t=0 to t=10.

I think that maybe I need to take the derivative of the equation but then what please help!
 
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  • #2
Hello mopar969,
mopar969 said:
How do you calculate the average velocity of the car for the time interval t=0 to t=10.
If you only need to find the average velocity, simply calculate the total distance traveled, divided by the time it takes to get there.
 
  • #3
Thank you. I can't believe that it was that simple. I was thinking instantaneous velocity that is why I was thinking about taking its derivative.
However, the question has another part to it that I am stuck on it says:

How long after stating from rest is the car again at rest? Please Help and Thanks.
 
  • #4
You're searching the time t when the velocity is 0.

x(t)= bt^2 -ct^3, this finds the displacement as a function of time. You'll need another equation (related to this one) to find the velocity as a function of time.
 
  • #5
Would I need the derivative of the displacement function?
 
  • #6
Yes that would give you the velocity.
 
  • #7
My next problem is how do I get t by itself?
 
  • #8
Never mind I realized that I could use the quadratic formula.
 

FAQ: Instantaneous Velocity Car Problem

1. What is instantaneous velocity in the context of a car problem?

Instantaneous velocity is the velocity of an object at a specific moment in time. In a car problem, it refers to the speed and direction of the car at a particular instant, rather than an average speed over a period of time.

2. How is instantaneous velocity calculated in a car problem?

Instantaneous velocity can be calculated by taking the derivative of the position function with respect to time. In a car problem, this would involve finding the first derivative of the car's position over time to determine its instantaneous velocity at a given time.

3. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement of an object over a period of time, divided by the time taken to travel that distance. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity provides information about its speed and direction at a particular instant.

4. How does acceleration affect instantaneous velocity in a car problem?

Acceleration is the change in velocity over time. In a car problem, if the car is accelerating, its instantaneous velocity will change over time. If the car is accelerating at a constant rate, its instantaneous velocity will increase or decrease at a steady rate. If the car is accelerating at a varying rate, its instantaneous velocity will change more rapidly.

5. Can instantaneous velocity be negative in a car problem?

Yes, instantaneous velocity can be negative in a car problem. This would indicate that the car is moving in the opposite direction of its initial motion. For example, if a car is initially moving forward and then begins to decelerate, its instantaneous velocity at some point during the deceleration may become negative, indicating that it is now moving in the opposite direction.

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