MHB Why Do Physics Equations Confuse Me So Much?

[lmae]

My brain feels like goop after reading these. I am struggling big time! Help is greatly appreciated.

Q1: The formula s=(u+v)/2t works out the distance traveled by an accelerating car (s), where u is the inital velocity, v is the final velocity and t is the time interval.
a) Transpose the formula, solving for v.
b) Find the velocity, v (metres/second, m/s) when s=400m, t=20s and u=30m.

Q2:An express train takes 5 1/2 hours to travel between two cities. If the express train takes only 3/5 of the time an ordinary train takes, how long will it take for the ordinary train to travel between the two towns?

 

[Joppy]

My brain feels like goop after reading these. I am struggling big time! Help is greatly appreciated.

Q1: The formula s=(u+v)/2t works out the distance traveled by an accelerating car (s), where u is the inital velocity, v is the final velocity and t is the time interval.
a) Transpose the formula, solving for v.
b) Find the velocity, v (metres/second, m/s) when s=400m, t=20s and u=30m.

Q2:An express train takes 5 1/2 hours to travel between two cities. If the express train takes only 3/5 of the time an ordinary train takes, how long will it take for the ordinary train to travel between the two towns?

Hello Imae :).

1a)

$$s = \frac{u+v}{2t}$$

Let's multiply both sides by $2t$, this gives,

$$s*2t = \frac{u+v}{2t} * 2t$$.

We can see that the 2t terms on the right hand side (RHS) will cancel giving us,

$$2ts = u + v$$

Subtracting u from both sides,$$2ts - u = u + v - u$$

$$2ts - u = v$$

Remember, whatever we do to one side, we must do to the other side. And in all of the above steps, we are working towards have v as our subject (in other words, we want the expression to be of the form 'v = something').

I have to go now, but hopefully this can get you started.

 

[HallsofIvy]

The formula s=(u+v)/2t works out the distance traveled by an accelerating car (s), where u is the inital velocity, v is the final velocity and t is the time interval.

Joppy did this problem assuming you meant [math]s= \frac{u+ v}{2t}[/math]. In fact, from physics, the correct formula is [math]s= \frac{u+ v}{2} t[/math]. That is a much simpler problem. To solve the equation v= At for t, divide both sides by A: t= v/A. In this case, [math]A= \frac{u+ v}{2}[/math]

Q2:An express train takes 5 1/2 hours to travel between two cities. If the express train takes only 3/5 of the time an ordinary train takes, how long will it take for the ordinary train to travel between the two towns?

Let "A" be the time for an express train, "B" the time for an ordinary train. If "the express train takes only 3/5 of the time an ordinary train takes" then E= (3/5)O and, dividing both sides by 3/5, O= (5/3)E. What is 5/3 of 5 1/2 hours?

 

[Joppy]

Joppy did this problem assuming you meant [math]s= \frac{u+ v}{2t}[/math]. [/math]

Ha! Whoops. I thought something seemed strange there, it's been awhile since I've dealt with these expressions. Thanks HallsofIvy, and apologies to the OP if any confusion was caused :).

 

[HallsofIvy]

Blast! I started off saying "Let "A" be the time for an express train, "B" the time for an ordinary train." but then switched to "E" and "O"!

I meant to say: If "the express train takes only 3/5 of the time an ordinary train takes" then A= (3/5)B and, dividing both sides by 3/5, B= (5/3)A. What is 5/3 of 5 1/2 hours?

 

[lmae]

Thanks for all your help guys. Got the train equation down pat. Not sure how I didn't understand that in the first place. Still have no idea what I am doing with question 1. (Not your fault Joppy, just really suck at maths) haha. How would I go about setting that question out? I find when I see the answer in front of me it is easy to find how we got to that solution but still struggle when it is looming around unanswered. I have given it another go and spoken to a lecturer who politely told me I was wrong in my final answer..