A speedboat travels in a straight line and increases in speed uniformly from vi

Question

A speedboat travels in a straight line and increases in speed uniformly from vi = 19.5 m/s to vf = 38.5 m/s in a displacement ?x of 165 m. We wish to find the time interval required for the boat to move through this displacement.

(a) Draw a coordinate system for this situation. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) What analysis model is most appropriate for describing this situation?
-particle under constant speed
-particle under constant acceleration
-particle in equilibrium

(c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat?
vf = vi + at
?x = vi + 1/2at^2

vf^2 = vi^2 + 2a?x

(e) Substitute numerical values to obtain the acceleration numerically.

(d) Solve the equation selected in part (c) symbolically for the boat's acceleration in terms of vi, vf, and ?x.
a = ?

(f) Find the time interval mentioned above.

Explanation / Answer

Here's what we know: initial velocity (u) = 20 final velocity (v) = 30 distance (s) = 200 Now we can apply an equation of straight line motion: v^2 = u^2 + 2as The only thing we don't know is acceleration 'a'. 30^2 = 20^2 + 2(a)(200) 900 = 400 + 400a 500 = 400a a = 1.25 ms^(-2) To find the time we'll use another equation for straight line motion: v = u +at 30 = 20 + 1.25t 10 = 1.25t t = 8 seconds 5 years ago

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