A boat enters the harbor at 14.1 m/s. Call this the positive direction. It needs to come to rest near the docks to begin docking. It is 62 m to the docking area

Question

acceleration equation 

Answer 1

Hi Madeline!

 

See your previous posted problem for a description of the technique I used for these kinematics problems.  In this case, it looks (though the question got munged a little bit in the posting) that we want to determine the acceleration the boat needs to accomplish the motion described.

 

to find: a

 

know:  d, v_o, v_f

 

d = 62 m (positive direction)

v_o = 14.1 m/s

v_f = 0

 

Why does v_f = 0?  Because the boat comes to rest at the end, and any time you see the words "at rest," it automatically (as you may be able to intuit) means v = 0 at that point.  In this case, it is at the end, so v_f = 0.

 

Then we choose the kinematic equation involving these four quantities, but NOT time, about which we know nothing at this point.  I would choose:

 

v_f² = v_o² + 2ad --> 0 = (14.1 m/s)²+2a(62 m)

 

This is an equation with the only unknown being acceleration, so you can solve for it.

 

Working out some of the algebra:

 

0 = 14.1² - 2(62)a --> 0 = 198.81 + 124a --> 124a = -198.81 --> a = -1.6 m/s²

 

Since the ship is traveling in the positive direction and slowing down (slowing down means velocity and acceleration have opposite signs), the acceleration is negative.

 

Again, just let me know if you want to check an answer or go into more detail!