Question

1) A speedboat increases its speed uniformly from vi = 20.0 m/s to vf = 36.0...

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

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