Question

1) A speedboat increases its speed uniformly from vi = 20.0 m/s to vf = 36.0 m/s in a distance of Δx = 2.40 ✕ 102 m.

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

(b) For the given information, what single equation is most appropriate for finding the acceleration? vf = vi + at a = vf − vi tf − ti Δx = vit + 1 2 at2 vf2 = vi2 + 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. s

2) A girl delivering newspapers covers her route by traveling 2.75 blocks west, 3.00 blocks north, and then 8.75 blocks east.

(a) What is her resultant displacement?

magnitude --------	blocks
direction ---------	° north of east

(b) What is the total distance she travels?
blocks

Answer 1

1)

a. You'll have to do the drawing yourself. It's single dimensional, just straight ahead displacement, velocity, and acceleration.

b. Use the kinematic formula Vf^2 = Vi^2 + 2*a*Δx

c. 2*a*Δx = Vf^2 - Vi^2

a = (Vf^2 - Vi^2) / (2*Δx)

d. Vf = 36 m/s. Vi = 20 m/s, and Δx = 240 m

Plug in the data and solve for a.

a = (36^2 – 20^2)/(2*240)

= 1.87 m/s^2

e. Use the kinematic formula

Vf = Vi + a*t

Plug in the data and solve for t.

t = (vf – vi)/a

= (36-20)/1.87

= 8.57 s