What are the velocity & position of an object as function of time?

In summary, a motorboat moving across a lake at a speed vo suddenly stops due to a frozen motor, slowing down under the frictional force fR = -bv. The velocity and position of the boat can be expressed as v=v0 e-b/m *t and x=x0+ v0m/b (1-e -b/m *t), respectively. To find the constant b/m, the given information from part (b) can be used to solve for the time it takes for the boat to stop and then plug into the equations.
  • #1
DANIneplanets
3
0

Homework Statement


A motorboat is moving across a lake at a speed vo when its moot suddenly freezes up and stops. The boat then slows down under the frictional force fR = -bv (a) What are the velocity and position of the boat as a function of time? (b) If the boat slows down from 4.0 to 1.0 m/s in 10s how far does it travel before stopping?

Homework Equations


fr=-bv

The Attempt at a Solution


v=v0 e-b/m *t
x=x0+ v0m/b (1-e -b/m *t)
 
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  • #2
Now use the information from part (b) to find the constant b/m
 
  • #3
how can i find b/m??
 
  • #4
Put the given information into equations:
v0e(-b/m)T = 4 m/s
v0e(-b/m)(T+10) = 1 m/s
Then you can find how long it takes to stop (which will depend on v0)
 

1. What is velocity?

Velocity is a measure of the rate of change of an object's position with respect to time. It is a vector quantity that includes both the speed and direction of an object's motion.

2. How is velocity related to time?

Velocity is directly related to time, as it is a measure of how an object's position changes over a specific period of time. The velocity of an object can change over time, resulting in a curved path.

3. What is position?

Position is the location of an object relative to a reference point. It is a vector quantity that includes both the distance and direction of an object from its starting point.

4. How is position related to time?

The position of an object can change over time, as it moves from one location to another. It is typically represented as a function of time, showing how the object's position changes over a specific period of time.

5. How do you calculate velocity and position as a function of time?

The velocity of an object can be calculated by dividing the change in position by the change in time. Similarly, the position of an object as a function of time can be determined by integrating the velocity function with respect to time.

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