Cars,acceleration,time and total displacement

Question

A car slows down from an initial velocity of 90km/h to a final velocity of 36.0 km/h at a constant rate while undergoing a displacement of 105m.

A) what is the acceleration?
B) if the car continues with same acceleration how much additional time will it take to come to a stop?
C) what is the total displacement of the car from instant when it travels at 90km/h until it stops?

Answer 1

Hi Alex!

 

As with previous kinematics problems we have worked on, the solution can be found by determining which among the kinematic quantities you want to find, and which you know, for each interval of interest.

 

In the first case, which kinematic quantity do we want to find?  I always ask this first, because it usually is spelled -- pretty much -- right out in the problem.

 

In A), they ask directly for the acceleration (assumed constant)

 

to find:  a

 

Then we find out, which three kinematic quantities do we know?

 

In A), we are told directly the initial velocity, the final velocity, and the displacement over the interval.  

 

know: v_o, v, (x-x_o)

 

Now, look for the kinematic equation that directly relates those four quantities.  I think you will find one that fits the bill is:

 

v² = v_o²+2a(x-x_o)

 

You can drop in the values you know, and solve for a.  Since the displacement is given in meters (and we usually calculate acceleration in the base unit of m/s²), it is probably worth converting those km/h velocities to m/s.   If you need help doing this, just let me know.

 

**********************************************************************************************

 

In B), we reset ourselves to look at a different interval.  Instead of considering an interval only to when the car goes from 90 km/h to 36 km/h, we now consider the interval over which it goes from 36 km/h to a stop.  

 

The question is, among what we know and what we want to find, what is different in B) compared to A)?

 

Look at what is being asked for:  the "additional time" to come to a stop.  This means we need to solve for the time it takes to go from 36 km/h to a stop.

 

to find: t

 

Over this interval, what do we know?  We know it starts at 36 km/h, and that it has the same (constant) acceleration in as in A).   These pieces of information are basically just stated int the problem.

 

know:  v_o, a

 

But what is s third thing we know?  Because we have already accounted for t (to find), v_o, and a (known), we have two choices:  displacement, and final velocity.  Do we know either one of those in this case?  The clue comes from the fact that the car comes to a stop at the end of this interval.

 

Once you figure out the third known, determine the kinematic equation that involves the four quantities known and to be found.  Then you can solve

 

*******************************************************************************************

 

In C), we reset the interval to look at the whole time the car goes from 90 km/h to a stop.  We can parse the problem the same way.

 

Which kinematic quantity over this interval is to be found?  (it is once again stated in the question)

Which three kinematic quantities do we know over this interval, given the information from all parts of this question?

Try setting this one up on your own, and see if it works.

 

I hope this sets you in the right direction.  If you want to go into more detail on any of these, or if you want to check any answers, just let me know!