Question

A speedboat starts from rest and accelerates at +1.98 m/s2 for 8.25 s. At the end of this time, the boat continues for an additional 5.58 s with an acceleration of +0.348 m/s2. Following this, the boat accelerates at -1.42 m/s2 for 7.22 s. (a) What is the velocity of the boat at t = 21.05 s? (b) Find the total displacement of the boat.

Answer 1

Vf = Vo + at,
Vf = 0 + 1.98m/s^2 * 8.25s = 16.34 m/s.
d1 = Vo*t + 0.5a*t^2,
d1 = 0 + 0.5*1.98*(8.25)^2 = 67.38 m.

Vf = Vo + at,
Vf=16.34 + 0.348 * 5.58s.=18.28 m/s^2.
d2 = Vo*t + 0.5a*t^2,
d2=16.34*5.58 + 0.5*0.348*(5.58)^2 = 96.6 m.

Vf = Vo + at,
Vf = 18.28 - 1.42*7.22 = 8.03 m/s.
d3=18.28 - 0.5*1.42*(7.22)^2=-18.73 m.

a. 8.03 m/s.

b. D = 67.4 + 96.6 - 18.73 = 145.3 m.