An iceboat has a constant velocity toward the east when a sudden gust of wind ca

Question

An iceboat has a constant velocity toward the east when a sudden gust of wind causes the iceboat to have a constant acceleration toward the east for a period of 3.0 s. A plot of x versus t is shown in the figure below, where t = 0 is taken to be the instant the wind starts to blow and the positive x axis is toward the east. (a) What is the acceleration of the iceboat during the 3.0 s interval? (b) What is the velocity of the iceboat at the end of the 3.0 s interval? (c) If the acceleration remains constant for an additional 3.0 s, how far does the iceboat travel during this second 3.0 s interval?

Explanation / Answer

a) The velocity of the boat at t= 0.5 is
v0.5  = (x0.5 - x0) / 0.5 - 0
v0.5  = (3 - 0) / 0.5
v0.5  = 6 m/s
The velocity of the boat at t = 3 s
v3   = (x3 - x2.5) / 3 - 2.5
v3  = (26 - 21) / 0.5
v3  = 10 m/s
The acceleration of the boat is
a = v3 - v0.5 / (2.5)
a = 10 - 6 / 2.5
a = 1.2 m/s2
b) The velocity of the iceboat at the end of the 3 s is
v3  = 10 m/s
c) Since the acceleration is constant, we can use the equations of motion
s = u t + (1/2) a t2
Where u is the initial velocity and a is the acceleration, t is the time taken, s is the distance traveled
We can assume that at time t =3 s as the initial time .The velocity of the boat at that time is found to be
u = 10 m/s
We have to find the distance traveled by the iceboat after t = 3 s
s = 10m/s x 3s + (1/2) x 1.2 m/s2 x (3 s)2
s =  35.4 m

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