I have the equation 'change in distance = 1/2 x (vf+vi) x change in time (or delta t)' for uniform acceleration. However, I am totally lost when it comes to rearranging it. I need to rearrange it for inital speed (vi) and change in time (delta t). Can someone please help?
That equation is a pretty basic one, it does hold true for uniform acceleration. Basically, the equation is
distance= average speed *time
where of course average speed is the average of starting and finishing speeds.
average speed= 1/2 (Vf+Vi)*time
If you want Vi, mulitiply both sides by 2, then divide both sides by time, finally, subtract Vf from both sides. This is basic algebra.
d=1/2 (vf+Vi)t
2d=(Vf+Vi)t
2d/t= Vf + Vi
2d/t -Vf= Vi
I will be happy to critique your rearrangement to solve for time.
If your algebra is this weak, you may want to consider getting a tutor on that. Discuss it with your teacher and parents.
In order to get the time, would I have to do the vf-vi divided by 2, times the distance??
I guess I really do need a brush-up on algebra!
**Oops, I meant vf+vi.
Is that the right equation?
Of course! I can help you with that. To rearrange the equation "change in distance = 1/2 x (vf + vi) x change in time" for initial speed (vi) and change in time (delta t), let's break it down step by step.
1. Start with the original equation:
change in distance = 1/2 x (vf + vi) x change in time
2. Distribute the 1/2 to both terms inside the parentheses:
change in distance = (1/2)vf + (1/2)vi x change in time
3. Subtract (1/2)vf from both sides of the equation to isolate (1/2)vi:
change in distance - (1/2)vf = (1/2)vi x change in time
4. Multiply both sides of the equation by 2 to eliminate the fraction (1/2):
2 x (change in distance - (1/2)vf) = vi x change in time
5. Simplify the equation further:
2(change in distance) - vf = vi x change in time
6. Finally, divide both sides of the equation by change in time to solve for vi:
vi = (2(change in distance) - vf) / change in time
So, the rearranged equation for initial speed (vi) and change in time (delta t) is:
vi = (2(change in distance) - vf) / change in time
Now, you can use this rearranged equation to calculate the initial speed when you have the change in distance, final velocity (vf), and change in time.