Solve Displacement Problem: 24 Rads

In summary, the conversation discusses the process of calculating displacement using a given graph. This involves finding the equation of the line, determining the angular velocity, and calculating the areas of the top and bottom triangles on the graph. The final displacement is found by subtracting the area of the bottom triangle from the area of the top triangle. The resulting displacement is 24 rad.
  • #1
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Homework Statement


http://img52.imageshack.us/img52/5412/displacement.jpg


The Attempt at a Solution


First I calculated the equation for the line using point-slope form. I got y = 3x-9. Then I found angula velocity at 8 seconds, which turned out to be 15 rad/s. Then I drew the complete graph and calculated area for the top triangle and the bottom triangle. For the top triangle I got a distance of 37.5 rad and for the bottome triangle I got a distance of 13.5 rad. To calculate displacement, I subtracted the area of the bottome triangle to the area of the top triangle and got 24 rad. Is this correct?
 
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  • #2
Yes, that's correct.
 

1. What is displacement?

Displacement is a vector quantity that measures the change in position of an object from its initial position to its final position.

2. How is displacement calculated?

Displacement can be calculated by subtracting the initial position from the final position. It can also be calculated using the formula: displacement = velocity x time or displacement = average velocity x time.

3. What is the unit of displacement?

The standard unit of displacement is meters (m) in the metric system and feet (ft) in the imperial system.

4. What does 24 rads mean in terms of displacement?

24 rads is a unit of measurement for rotation, not displacement. It represents 24 radians, which is equivalent to approximately 1372.32 degrees.

5. How is displacement different from distance?

Displacement is a vector quantity that only measures the change in position, while distance is a scalar quantity that measures the total path traveled. Displacement takes into account direction, while distance does not.

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