Total distance traveled by particle


by BrownianMan
Tags: distance, particle, traveled
BrownianMan
BrownianMan is offline
#1
Mar4-10, 04:23 PM
P: 134
If s(t) = 2t^3 - 21t^2 + 60t is the position function of a particle moving in a straight line, would you be able to find its total distance traveled in, say 3 seconds, by finding s(0), s(1), s(2), s(3), and calculating the absolute value between each of them and then summing those values, as opposed to differentiating the function first, setting the derivative to 0, and solving for t?

Would you get the same answer?
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sjb-2812
sjb-2812 is offline
#2
Mar4-10, 04:27 PM
P: 418
What do you hope to gain by setting ds/dt to 0?
BrownianMan
BrownianMan is offline
#3
Mar4-10, 04:38 PM
P: 134
That's the standard way of solving such a problem - or at least how we've been taught. You differentiate to find the velocity, then set velocity to 0 to find the intervals when the particle is moving in a positive and in a negative direction.

sjb-2812
sjb-2812 is offline
#4
Mar5-10, 11:59 AM
P: 418

Total distance traveled by particle


OK, just making sure you understand. What would happen in both cases if the function was say, s(t) = 4t2-4t+1?


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