Can the Average Velocity Equation be Simplified Further?

[noname1]

I need to calculate the average velocity of

d= Et²+Ft+G over the interval [t1;t2]

I after resolving i get to this function

avg v = (E(t2)² + Ft2 - E(t1)² + Ft1) / (t2-t1)


my question is it possible to go any further than this?

 

[Mark44]

Your average velocity has an error. The Ft₁ term in the numerator should be -Ft₁. After you fix that, you can simplify your expression.

avg v = (E(t2)² + Ft2 - E(t1)² - Ft1) / (t2-t1)
= [E(t₂² - t₁²) +F(t₂ - t₁)]/(t₂ - t₁)

Now factor (t₂ - t₁) out of each term in the numerator, and you can cancel with the same factor in the denominator.

 

[noname1]

yea i for got to distribute the - sign

would this be it?

[t2 - t1 (E(t2-t1) + F)]/ t2 - t1 and than the solution would be

(E(t2-t1) + F)

correct?

 

[Mark44]

No. a² - b² = (a - b)(a + b).

 

[noname1]

than like this

[E (t2-t1)(t2+t1) + F (t2-t1)] / t2-t1 =

than i can cancel the top (t2-t1) with the bottom giving

E (t2-t1) + F

 

[Mark44]

No again.

Also, you should write your expression this way: [E (t2-t1)(t2+t1) + F (t2-t1)] / (t2-t1)

 

[noname1]

crossed out the wrong one, i meant

[E (t2+t1) + F] correct?

 

[Mark44]

Yes, that's better.

 

[noname1]

and than for instantaneous i would take the derivative which is

2et² + f correct?

 

[Mark44]

Yes, but I would use the same letters as in the original problem.
v = 2Et² + F

 

[noname1]

thanks for your help, now just have to figure out my other thread