1
$\begingroup$

Hi I have just started my GCSE Physics and Maths course and I am hoping to confirm my understanding of the formula to calculate acceleration. Now I understand $a= \frac{(v_f - v_i)}{t}$. However I am not sure how I use this formula or change it to accomodate the following question.

A toy car is acceleratingat $2\frac{m}{s^2}$. It starts at a velocity of $5\frac{m}{s}$. What will its velocity be after $3s$?

I didn't know how to rearrange the formula to answer the question, so I just thought it through (so im sure its probably wrong). Could someone say yes/no and explain or link me to an explination to this scenario?

So my thinking was, if its traveing at $5\frac{m}{s}$ for $3s$ that would be $6\frac{m}{s}$ plus the initial velocity of $5\frac{m}{s}$. So the answer is $11\frac{m}{s^2}$?

2 Answers 2

2

Let's work on $a = \frac{v_f - v_i}{t}:$

$$a = \frac{v_f - v_i}{t} \Rightarrow \\ \Rightarrow a \cdot t = v_f - v_i \Rightarrow \\ \Rightarrow v_f = a \cdot t + v_i.$$

Since $a = 2$, $v_i = 5$ and $t = 3$, then:

$$v_f = 2 \cdot 3 + 5 = 11 \frac{m}{s}.$$

Long version

Your objective is to find out $v_f$ (this is what the problem is asking to you). Then do something to obtain $v_f = $ something... Let's start!

$$a = \frac{v_f - v_i}{t}$$

First step: multiply both side by $t$: $$a \cdot t = \frac{v_f - v_i}{t} \cdot t.$$

Second step: simplify $t$ on the right hand side: $$a \cdot t = v_f - v_i.$$

Third step: add $v_i$ to both side:

$$a \cdot t + v_i= v_f - v_i + v_i.$$

Fourth step: simplify $v_i$ on the right hand side

$$a \cdot t + v_i= v_f.$$

Fifth step: invert the order of the equation:

$$v_f = a \cdot t + v_i$$.

Notice that these are very elementary algebraic steps...

  • 0
    Initially, how do I type out the formula like above? My original question was modified to include the nicely formatted equations. Secondly, ok so I worked it out correctly, great. But I would like to understand how to rearrange the formula to calculate the answer. For instance how would I know to multiply the a by t ? I know it seems kind of obvious but there must be away to KNOW thats what is needed? Jesus does that even make sense? lol – 2017-01-16
  • 0
    Arr I may have worked it out using this method https://www.youtube.com/watch?v=BpLHHTY_umM . If a = (vf-vi)/t. We move t to a.t and vi below a.t so a.t /vi however this becomes a addition as it was originally a minus. so a.t + t = 11 ? Is that correct rearrangement ? – 2017-01-16
  • 0
    @iNoob I have updated my answer. Please take look now and let me know if this clarify your mind. – 2017-01-16
  • 0
    Yes thats great thank you, I appreciate the brevity and yes I know im quite stupid :( "Finally, these are elementary algebraic steps..." – 2017-01-16
  • 0
    O, before I leave and accept the answer, how do I type out the formual/equations as illustrated in this post? – 2017-01-16
  • 1
    @iNoob you are not stupid. Trust me, all questions are not stupid! I suggest you not to be afraid... algebra is your friend, and paper/ink are cheap :D keep training yourself! – 2017-01-16
  • 1
    @iNoob the general rule is to enclose your formulas between dollar signs ($\$$) – 2017-01-16
  • 0
    test $a=(vf-vi)/t$ – 2017-01-16
  • 0
    hmm how do I do a horizontal line to reprosent divide ? – 2017-01-16
  • 1
    @iNoob take a look [here](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) – 2017-01-16
  • 0
    holly crap, ok Ill have to get use to that, ill try find a key or cheatsheet online. Thanks again for the verification and explinations – 2017-01-16
2

Yes, you did it right.

One thing that helps give confidence is to check your units. Here, you multiplied $2 \frac{\mbox{m}}{\mbox{s}^2} \cdot 3 \mbox{s} = 6 \frac{\mbox{m}}{\mbox{s}} $ so you know your units are fine.