A sailboat starts from rest and accelerates at a rate of 0.13 m/s2 over a distance of 458 m.

(a) Find the magnitude of the boat's final velocity.

m/s

(b) Find the time it takes the boat to travel this distance.

s

Given:

u (initial velocity) : 0

a (acceleration) : 0.13 m/s∧2

distance = 458 m

Now s = ut + 1/2 (at∧2)

Substituting from the given values we get

458 = 0 + 1/2 (0.13 x t∧2)

t = 83.94 secs

Now v (velocity) = u + at

Substituting for t as 83.94 secs and for a and u from the given values we get:

v = 0+0.13 x t

v = 0.13 * 83.94

v=10.91 m/s

Therefore the final velocity of the boat is 10.91 m/s and the time taken for the boat to travel 458 m is 83.94 secs