A sailboat is traveling to the right when a gust of wind causes the boat to accelerate leftward at 2.5m/s2 for 4s. After the wind stops, the sailboat is traveling to the left with a velocity of 3.0m/s.
Assuming the acceleration from the wind is constant, what was the initial velocity of the sailboat before the gust of wind?
Answer using a coordinate system where rightward is positive.

Taking right movement to be positive means leftward movement is negative.
Hence we have a deceleration of
[tex]a = - 2.5 {ms}^{ - 2} [/tex]

[tex]t = 4s[/tex]
[tex]v = 3.0 {ms}^{ - 1} [/tex]
Using this 'suvat' equation
[tex]v = u + at[/tex]
we can determine the initial velocity

[tex]3.0= u + -2.5(4)[/tex]

[tex]3.0+2.5(4)=u[/tex]

[tex]13.0 = u [/tex]

Hence the initial velocity is 13.0 meters per seconds

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shirleywashington shirleywashington · Answer 2 · 2019-04-01T07:07:50+02:00

Explanation :

Let rightward direction is considered as positive and leftward direction is considered as negative.

Given that,

Acceleration of the boat, [tex]a=-2.5\ m/s^2[/tex] ( in left )

Time taken, [tex]t=4\ s[/tex]

Final velocity of the boat, [tex]v=-3\ m/s[/tex]

We have to find initial velocity (u) of the sailboat.

Using first equation of motion :

[tex]v=u+at[/tex]

[tex]u=v-at[/tex]

[tex]u=-3-(-2.5)\times 4[/tex]

[tex]u=-13\ m/s[/tex]

So, initially the boat is moving with a speed of 13 m/s in leftwards direction.

Hence, this is the required solution.