What is the displacement of the particle

In summary, the conversation discusses the problem of finding the displacement of a particle given its velocity function. The approach is to use integration, with the limits of integration being the given time intervals. The formula for position is derived from the velocity function, and the unknown constant is cancelled out when evaluating at the given time intervals. The conversation also touches on the reason for the seemingly large answer due to the rapidly increasing speed.
  • #1
ffrpg
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Here's my problem, The velocity of a particle is given by
v = (5.5 m/s^4)t^3 - (5.4 m/s), what is the displacement of the particle during the interval t=3.5s to t=9.0s? I don't even know if I started it off right. I recalled seeing something similar to this in calc, so I tried integrating the formula given using 3.5 as 'a' and 9.0 as 'b'. I ended up getting 80440.5 as my answer, but it seems a bit large. I just need to know how to approach the problem. Thanks
 
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  • #2


"a" and "b"? I don't understand what those are! Oh, you mean the limits of integration. That's exactly what you should do.

What you need to know is that velocity is the derivative of position so position is the anti-derivative of velocity- that is, the integral.

Since v= dx/dt= (5.5)t^3 - 5.4, x= (5.5/4)t^4- 5.4t+ x0. (x0 is the "unknown constant" and would be the position of the particle at t=0). Evaluate at t= 9.0s and t= 3.9s and subtract. (The x0 in each term will, of course, cancel).

Why does your answer seem "a bit large"? With the t^3 term the speed is going to increase rapidly!
 
  • #3
Hey thanks for the help. I figured out what I did wrong. I integrated incorrrectly. THANKS!
 

1. What is displacement?

Displacement is a measure of the change in position of an object or particle. It is a vector quantity, meaning it has both magnitude and direction.

2. How is displacement different from distance?

Displacement is a specific type of distance that takes into account the direction of movement. Distance is a scalar quantity that only measures the total amount of ground covered.

3. How is displacement calculated?

Displacement is calculated by finding the difference between an object's initial position and its final position. This can be represented by the equation d = xf - xi, where d is displacement, xf is the final position, and xi is the initial position.

4. Does displacement have a unit of measurement?

Yes, displacement is typically measured in units of length, such as meters (m) or feet (ft).

5. Can displacement be negative?

Yes, displacement can be positive, negative, or zero. A positive displacement indicates movement in one direction, while a negative displacement indicates movement in the opposite direction. A displacement of zero means there is no change in position.

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