A boat accelerates from 17.2 m/s with a rate of 1.3 m/s2 for a time of 5.4 s. What is the final velocity of this boat?

Question

 Physics velocity equation 

Answer 1

Hi Madeline!

 

Kinematics, the subject of this problem, is the study of motion using five key quantities:  acceleration (a), initial velocity (v_o), final velocity (v_f), displacement (d), and time (t).  Usually, a problem asks you to solve for one of these quantities.  You should have four equations at your disposal, relating these five quantities.  Each equation involves four of the five quantities.  Therefore, if you want to use the equations to solve for one of the kinematic quantities, you have to know at least three others for the given situation.  The challenge of kinematic problems is usually finding out what information you are given.

 

The way I usually work these problems is to ask, first, which of the five kinematic quantities is being asked for?  This is often easiest to pick out, because the question has to directly state it.  For the problem above, the last sentence clearly asks for the final velocity of the boat (v_f).  So

 

to find:  v_f

 

Now, we have to know three other kinematic quantities.  Which ones are those?  We are told acceleration = 1.3 m/s², the time interval of this motion is 5.4 s, and the boat accelerates "from" 17.2 m/s, meaning 17.2 m/s is the initial velocity of the boat over the period of interest.  So we have

 

know:  a, t, v_o

 

a = 1.3 m/s²

t = 5.4 s

v_o = 17.2 m/s

 

Now, we have the three known kinematic quantities we need.  The next step is to determine which kinematic equation includes all four of these quantities, but NOT displacement, about which we know nothing yet.  The equation I would use is:

 

v_f = v_o+at -->  v_f = 17.2 m/s + (1.3 m/s²)(5.4 s) 

 

This lets you solve for v_f.  This kinematic equation, by the way, is basically just a rearrangement of the definition of acceleration.

 

I hope this helps!  Let me know if you have other questions about this.