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**[SOLVED]Constant Acceleration problem**

## Homework Statement

When a high speed train traveling at

**161 km/hr**rounds a bend,he is shocked to see that a locomotive has improperly entered onto the track at a distance

**D=676 m**ahead. The locomotive is moving at

**29.0 km/hr**away from the train. The engineer of the train immediately applies the brakes. What must be the magnitude of the resulting deceleration if a collision is just to be avoided?

## Homework Equations

a=C

v= vi+a*t

x=xi+vt+(1/2)*a*t^2

## The Attempt at a Solution

First i convert the speed of the train and the locomotive to m/s:

train: 44.7 m/s

Loco: .806 m/s

Next I make a system of eq. for x

x= (0)+(44.7)*t+.5*a*t^2 [kinematic equation]

x= (676) + .806*t {Ini. spacing add the distance trav. by Loc}

Now I combine the two

676= 43.9*t+.5*a*t^2

next I solve for a with respect to t

0 = 44.7+a*t [kinematic equation]

a = -44.7/t

and substitute and solve for t

676= 43.9*t - .5*(44.7*t)

t= 31.3

now I solve for a

a= -44.7/(31.3) [kinematic]

a= -1.42 m/sec^2 ANSWER

However the book gives something different (.994 m/sec^2), I think I'm screwing up in determining the time. Can someone help me in determining my error. Thanks in advance

edit: to make it less confusing

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