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A speedboat increases its speed uniformly from vi = 20.0 m/s to vf = 33.0 m/s in a distance of Δx = 2.40 ✕ 102 m.vf2 = vi2 + 2a(Δx)a) solve the equation above symbolically for the boat's acceleration in terms of vf, vi, and Δx.b) Substitute given values, obtaining the acceleration.c) Find the time it takes the boat to travel the given distance.

Question

A speedboat increases its speed uniformly from vi = 20.0 m/s to vf = 33.0 m/s in a distance of Δx = 2.40 ✕ 102 m.

vf2 = vi2 + 2a(Δx)
a) solve the equation above symbolically for the boat's acceleration in terms of vf, vi, and Δx.
b) Substitute given values, obtaining the acceleration.
c) Find the time it takes the boat to travel the given distance.
check_circleAnswer
Step 1

a)

The expression connecting squares of final and initial velocities, acceleration and displacement is,

=v +2aAr
2aAr
a
2Ax
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=v +2aAr 2aAr a 2Ax

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Step 2

Answer: a=(vf2- vi2))/2∆x

Step 3

b)

Substituting the...

(33.0m/s)-(20.0m/s)
2(2.40x102
689 m2/s2
480m
=1.43m/s2
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(33.0m/s)-(20.0m/s) 2(2.40x102 689 m2/s2 480m =1.43m/s2

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