A pontoon boat travels across a lake in a straight line and increases in speed uniformly from vi = 18.5 m/s to vf = 36.0 m/s in a displacement Δx of 250 m. We wish to find the time interval required for the boat to move through this displacement. g (a) Draw a coordinate system for this situation.

(b) What

analysis model is most appropriate for describing this situation?

(c) From the analysis model, what equation is most

appropriate for finding the acceleration of the speedboat?

(d) Solve the equation selected in part (c) symbolically for

the boat’s acceleration in terms of vi , vf , and ?x. (e) Substitute

numerical values to obtain the acceleration numerically.

(f) Find the time interval mentioned above.

Explanation:

a ) The motion is one dimensional , so motion is along x - axis , starting from origin ( 0 , 0 )

b ) Initial velocity is 18.5 m /s when boat is situated at origin . When he displaces by 250 m along x axis and his position is ( 250 , 0 ) along x axis , his velocity becomes 36 m /s . Both his velocity and acceleration is along x - axis.

c ) Initial velocity vi = 18.5 m /s

final velocity vf = 36 m/s

Displacement x  = 250 m

Acceleration a = ?

Most appropriate formula is given below .

vf² = vi² + 2 a x

2ax = vf² - vi²

x =  ( vf² - vi² ) / 2 a

d )

Putting the given values

36² - 18.5² / 2 x 250

= 1296 - 342.25 / 500

= 1.9 m /s².

f ) Time interval t = ?

Required formula

vf = vi + at

t = (vf - vi ) / a

Putting the values

t = (30 - 18.5) / 1.9

= 6.05 second .

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