In this article, the topic is the relationship between

How do you find a total displacement when given time (t), initial displacement (di), initial velocity (vi), but instead of acceleration (a), you are given force (F) and mass (m)?

**Newton's Second Law and Motion,**and this time,**displacement**will be the focus.How do you find a total displacement when given time (t), initial displacement (di), initial velocity (vi), but instead of acceleration (a), you are given force (F) and mass (m)?

Once again, it is necessary to combine two principles in order to see the full relationship.

The distance formula is:

*df =*

*di +*

*(vi )(t)+ 1/2(a)(t*

^{2})However, to find final displacement, you need an acceleration(a), but you have mass and force.

Using Newton's Second Law, fortunately, will allow the calculation of a using the force and mass given.

**So, we'll be doing two steps.**

Step 1:

Use

*F=ma*to find a

Step 2:

Then use THAT in the distance formula.

*df =*

*di +*

*(vi )(t)+ 1/2(a)(t*

^{2})
EXAMPLES

Example 1

Let's take a look at another example (even easier!) and work it out:

*A force of 50 N acts on a object with a mass of 10 kg. If it has an initial displacement (di) of 10 m and has an initial velocity (vi) of 20 m/s, what is its final displacement after an elapsed time of 4 seconds?*

The question tells us that we need to find final velocity (vf). But there is no acceleration given. So, do step 1 (above):

Find a where:

F = 50 N

m = 10 kg

*F = ma*

*50 N = (10 kg)(a)*

*50 N/10 kg = a*

*5 m/s/s = a*

Next, use THAT calculated a to find final velocity (step 2 above):

Find df where

di = 10 m

vi = 20 m/s

t = 4 s

a = 5 m/s/s

*df =*

*di +*

*(vi )(t)+ 1/2 (a)(t*

^{2})*df = 10 m*

*+*

*(20*

*m/s )(4 s)+ 1/2 (5 m/s/s)(4*

^{2})*df = 10 m*

*+*

*80 m + 1/2 (5 m/s/s)(16 s*

^{2}*)*

*df = 10 m*

*+*

*80 m + 40 m*

*df = 130 m*

How about

*seeing one*worked out?
SUMMARY:

You gotta do it in steps!

This process requires doing the work in steps. Depending on what is given, you use the two formulas below:

*F = ma*

*df =*

*di +*

*(vi )(t)+ 1/2(a)(t*

^{2})
So, read the problem, write down what is being looked for, write down what is given, THEN... use the two formulas. Two steps!