derivation of kinematic equations
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Answers:d = vi * t + .5at^2 vf = vi + at so, rearranging the second equation, vi = -at + vf plug that in for vi in the first d=(-at + vf)t + .5at^2 From here, just plug&chug and it should result in a final speed of 3.097 m/s towards the tree. Plug it back into the second equation, and you will find that the initial velocity is 26.617 m/s. Not that vi matters, or anything :)
Answers:Do you know about integrals and primitives? Now seeing the formulas you have there it is very straightforward. d=1/2 (Vi+Vf)t=1/2(vi+vi+at)t=vi.t+1/2at The second formula we derive by eliminating the time t=2d/(vi+vf). d=vi 2d/(vi+vf)+a/2.(2d/(vi+vf)) Simplifying this form you will indeed get: vf =vi +2ad. Yet this yields more of mathematical exercice than real physical reasoning. In fact the first formule would be derived by integrating, as follows: d=o$t o$t a.dt=do+vi.t+at /2 and you have declared do=o.
Answers:The equation for displacement is x = 4.9*t^2 + Vo*t where t is time and Vo is the initial velocity. The equation for velocity V=a*t where a is acceleration (gravity=9.81m/s^2) Rearrange equation to solve for Vo, giving Vo= (x-4.9*t^2)/t Sub in values for x (length of the window), and t. Vo=16.78m/s Use V=a*t to find time taken to travel from rest to Vo, t=16.78/9.81 t=1.71 Now sub that time back into x=4.9*t^2, which gave me a value of 14.3
Answers:This is the second equation of motion in which you have S, t, a and Vi.. d is distance, t is time, a is acceleration and Vi is initial velocity... d = Vit + 1/2at When you handle problems which have bodies dropped from some height ( free fall ) or which have bodies accelerating from rest then their Initial velocity is zero.. d = (0)t + 1/2at ...............( Any number or variable multiplied by zero = zero ) d = 0 + 1/2at d = 1/2at 2d = at ......(1 is being divided by 2 or right side, so when we move it to left side we multiply it) 2d/a = t ...........................( a is multiplied by t so we write it in division on left side ) Taking sqrt both sides... 2d/a = t .....................( over t is canceled by ) => t = 2d /a