In the particle under constant acceleration model, we identify the variables and

Question

In the particle under constant acceleration model, we identify the variables and parameters vxi, vxf , ax, t, and xf ? xi. Of the equations in the table below, the first does not involve xf ? xi, the second does not contain ax, the third omits vxf , and the last leaves out t. So, to complete the set, there should be an equation not involving vxi. (a) Derive it from the others. (Use any variable or symbol stated above as necessary.) xf ? xi = (b) Use the equation in part (a) to solve the following problem in one step. The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with an acceleration of -5.59 m/s2 for 4.01 s, making straight skid marks 56.9 m long, all the way to the tree. With what speed does the car then strike the tree? m/s

Explanation / Answer

There are two constant acceleration equations that are worth remembering. You can always decide not to remember any, and derive these two using calculus, but assuming you don't want to start every constant-acceleration problem with calculus, you should know

xf = xi + vxi t + ½ ax t²

vxf = vxi + ax t

all the rest of "the set" can be derived using algebra.

To eliminate vxi, I'd solve the second equation for it

vxi = vxf - ax t

and substitute it into the first one:

xf = xi + (vxf - ax t) t + ½ ax t²

I suppose the creators of idiotic tables would prefer this to be simplified

xf = xi + vxf t - ½ ax t²

PLEASE RATE ME IF THE SOLUTION HELP YOU

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