Use the exact values you enter in previous anwers to make later calculations. A

Question

Use the exact values you enter in previous anwers to make later calculations. A barge on a still lake is moving toward a bridge at 10.0m/s. When the bridge is 36.0m away, the pilot slows the boat with a constant acceleration of -0.79m/s^2.

a) use x = x0 + v0t + 1/2at2 to find the time it takes the barge to reach the brige. Note that you will obtain two answers.t1=?s t2= ?s

Do both calculated times correspond to possible physical situations? Yes or No

b) find the final velocity for each time using v = v0 + at.

v(t1)= ?s v(t2)= ?s

c) use the two sets of answers for t and v to sketch a plot of velocity versus time.

d) Use the two sets of answers for t and v to sketch a plot of position versus time. (Assume the bridge is located at the origin such that the x = ?36.0 m is the initial position of the barge.)

Explanation / Answer

a) 36 = 0+ 10t + (0.5)(-0.79)t^2 => 36 = 10t - 0.395 t^2 => 0.395t^2 - 10t + 36 = 0 So, t1 = [10+{10^2-4*0.395*36)^1/2]/(2*0.395) = 20.97 s also, t2 = [10-{10^2-4*0.395*36)^1/2]/(2*0.395) = 4.346 s both are possible physical situations.. In 1st case the barge reaches bridge at t2 = 4.346 s, then keeps on going till its velocity is zero, and then starts coming back and again reaches bridge at t1=20.97 s b) v1 = -6.5663 m/s v2 = 6.567 m/s c) the plot will be a straight line.. vv on y-axis and t on x-axis.. v starting from 10 m/s, then a downward sloping line till v=0 at t=12.66 s, then again a upward sloping straight line till t2=20.56 s and v = 6.667 m/s

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