Question

A sailboat starts from rest and accelerates at a rate of 0.21 m/s^2 over a distance of 280 m. find the magnitude of the boat's final velocity. find the time it takes the boat to travel this distance.

Answer 1

We use the kinematic equations,

$v=u+at$                                          (A)

$S= ut + \frac{1}{2} at^2$                  (B)

Here, u is initial velocity, v is final velocity, a is acceleration and t is time.

Given,  $u=0$, $a=0.21 \ m/s^2$ and $s= 280 m$.

Substituting these values in equation (B), we get

$280 \ m = 0 +\frac{1}{2} (0.21 m/s^2) t^2 \\\\ t^2 = \frac{280 \times 2}{0.21 } \\\\ t= 51.63 \ s$.

Therefore from equation (A),

$v = 0 + (0.21) \times (51.63 s)= 10.84 \ m/s$

Thus, the magnitude of the boat's final velocity is 10.84 m/s and the time taken by boat to travel the distance 280 m is 51.63 s