A speedboat increases its speed uniformly from v i = 20.0 m/s to v f = 29.0 m/s

Question

A speedboat increases its speed uniformly from

vi = 20.0 m/s

to

vf = 29.0 m/s

in a distance of

x = 1.90 102 m.

(a) Draw a coordinate system for this situation and label the relevant quantities, including vectors.

(b) For the given information, what single equation is most appropriate for finding the acceleration?

vf = vi + at

vf2 = vi2 + 2a(x)

    a =

x = vit +

at2
(c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms of vf, vi, and x.
a =

(d) Substitute given values, obtaining the acceleration.
m/s2

(e) Find the time it takes the boat to travel the given distance.
s

Explanation / Answer

Given,

Vi = 20 m/s

Vf = 29 m/s

x= 190 m

b) Using kinematic equation,

Vf^2 = Vi^2 + 2a x

c) a = (Vf^2 - Vi^2) / (2x)

d) a = (29^2 - 20^2) / (2 x 190) = 1.16 m/s^2

e) x = 1/2(t)(Vf + Vi)

190 = 1/2 (t) (29 + 20)

190 = 24.5 t

Time, t = 7.76 sec

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