Question

A speedboat increases its speed uniformly from vi = 20.0 m/s to vf = 29.0 m/s in a distance of Δx = 1.60 ✕ 102 m.

(a) Draw a coordinate system for this situation and label the relevant quantities, including vectors.

A speedboat in two positions is shown. The speedboat on the left has a speed vi with its vector pointing to the right. The speedboat on the right is at a distance of Δx (in meters) from the speedboat on the left and has a speed vf with its vector pointing to the right. The length of this vector is smaller than that of vi.

A speedboat in two positions is shown. The speedboat on the left has a speed vi with its vector pointing to the right. The speedboat on the right is at a distance of Δx (in meters) from the speedboat on the left and has a speed vf with its vector pointing to the left. The length of this vector is larger than that of vi.

A speedboat in two positions is shown. The speedboat on the left has a speed vi with its vector pointing to the right. The speedboat on the right is at a distance of Δx (in meters) from the speedboat on the left and has a speed vf with its vector pointing to the right. The length of this vector is larger than that of vi.

A speedboat in two positions is shown. The speedboat on the left has a speed vi with its vector pointing to the left. The speedboat on the right is at a distance of Δx (in meters) from the speedboat on the left and has a speed vf with its vector pointing to the left. The length of this vector is larger than that of vi.

(b) For the given information, what single equation is most appropriate for finding the acceleration?

a = vf − vi / tf − ti

Δx = vit + 1/2 at2

vf = vi + at

vf^2 = vi^2 + 2a(Δx)

(c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms of vf, vi, and Δx.

a =

(d) Substitute given values, obtaining the acceleration. m/s2

(e) Find the time it takes the boat to travel the given distance.

Answer 1