Finding Deceleration to Avoid Collision

[smthbrothrJ]

[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

 

[Doc Al]

First i convert the speed of the train and the locomotive to m/s:
train: 44.7 m/s
Loco: .806 m/s

That last one should be: 8.06 m/s.

 

[smthbrothrJ]

AH I see. Thanks for the proofread, now I know to double check the math as well as the concept too!