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## Homework Statement

Vehicle A and Vehicle B are moving in opposite directions on the NJTP. Vehicle A is heading south toward atlantic city while vehicle B is heading north towards Hoboken. In situation 1 and 2 described below, at t = 0s both vehicles are at a distance of separation of 400m and are moving towards each other.

Situation 1: When vehicle A is moving at a constant velocity of 30 m/s and travels a distance of 120 m, the vehicles pass each other on the turnpike.

Situation 2: When vehicle A is moving at a constant velocity of 80 m/s and after a time of 3s, the vehicles pass each other on the turnpike.

For vehicle A label variables as: Via, Vfa, aa, da,ta

For vehicle B label variables as: Vib, Vfb, ab,db, tb

In the ORDER INDICATED:

(a) Calculate the initial velocity of vehicle B or Vib; and

(b) Then calculate the acceleration of vehicle B or ab

Show all work in DETAIL and keep all numerical values to the nearest hundredth value. Draw and label all pictures

Note: You will receive NO CREDIT if you first calculate part (b) and then part (a)

For situations 1 and 2

vib = constant ; vfb ≠ a constant value since its value changes w/ time

ab = constant

## Homework Equations

## The Attempt at a Solution

__Situation 1:__Da + Db = 400

Via = 30 m/s

Vfa = 30 m/s

a = 0 m/s2

da = 120 m

ta = ?

Vave = d/ t = vf + vi /2

Vave = da/ta

ta = 4s

db = 280

ta = 4s

__Situation 2:__Via = 80 m/s

aa = 0 m/s2

vfa = 80 m/s

ta = 3s = tb

da = ?

Using same equation as in situation 2,

da = 240

db=160

tb = 3s

__Situation 1__d

_{b}= vi

_{b}t

_{b}+ 1/2a

_{b}t

_{b}

^{2}

280 = vi

_{b}(4) + 1/2 (a

_{b})(4)

^{2}

__Situation 2__d

_{b}= vi

_{b}t

_{b}+ 1/2a

_{b}t

_{b}

^{2}

280 = vi

_{b}(3) + 1/2 (a

_{b})(3)

^{2}

280 = vi (4) + 8ab

280 - 4bi = 8ab

280 - 4vi/8 = ab

Plug this into the second equation...

160 = vib(3)+ 1/2 (280 - 4vi/8 )9

I solve and get vib = - 4/3 m/s which doesn't make sense...

So i plug that answer back into the two equations above and get ab = 35.67 m/s2 for situation 1 and for situation 2 - 34.67 m/s2.

Thank you for the help