# I cant solve a simple Acceleration/Deceleration rate of time problem.

A train with a maximum speed of 105km/h has an acceleration rate of 0.25m/s² and a deceleration rate of 0.7 m/s². Determine the minimum running time between stations 7km apart, if it stops at all stations.

We are using the basic kinematics equations.
S= VoT + 1/2aT²
V=Vo +aT
V² = Vo² +2as

My main problem is what would acceleration be considered, I am giving two variables.
.25m/s² and -0.7 m/s².

So far I have S= 7km which I converted to 7000m
V= 105 km/h which I converted to 29.16m/s

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first find the distance train travels while it accelerates to max velocity and also distance is travels while decelerating from max velocity to 0 .. rest distance left is traveled at max velocity.

Find corresponding times and add them

Ok first I took the kinematics equation V=Vo+at

29.16m/s= 0+(.25m/s²)t

T= 116.6s for the train to accelerate to a full velocity of 29.16m/s
S = 1700M for the train to travel to full acceleration.
So there is a distance of 5300M left to go.

It takes the train 607.3M to go from full velocity to 0.
T= 41.6s

4692.7M to go.

so at full velocity of 29.16m/s
I divide the 4692.7 M by 29.16m/s to get a time of 160s...

Man is there a easier way to do this, like more kinematics formulas that I might need to know?

I'm afraid No