Question

A sailboat is traveling to the right when a gust of wind causes the boat to accelerate leftward at 2.5​​​​m​​/s2 for 4s. After the wind stops, the sailboat is traveling to the left with a velocity of 3.0​m/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.

Answer 1

Explanation :

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

Given that,

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

Time taken, $t=4\ s$

Final velocity of the boat, $v=-3\ m/s$

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

Using first equation of motion :

$v=u+at$

$u=v-at$

$u=-3-(-2.5)\times 4$

$u=-13\ m/s$

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

Hence, this is the required solution.

Answer 2

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

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

$3.0= u + -2.5(4)$

$3.0+2.5(4)=u$

$13.0 = u$

Hence the initial velocity is 13.0 meters per seconds