To understand acceleration, you need to know speed and velocity.
Why?
Acceleration is the change in velocity, and the velocity equation is:
velocity = distance / time Units: (m/s)
If a change in position means an object has a velocity, then that means that a change in velocity has an acceleration (I recommend you look at the graphs, it will help a lot to understand the relationship between each).
Now that we have some background, lets use it to answer the problem!
The change in velocity is from 25 m/s to 10 m/s, and we have a time. Lets plug it into the (average) acceleration equation so we can visualize it better!
The symbol delta means "change" : Δ
a = Δv / Δt
expanded to:
a = vf - vi / tf - ti
(vf = velocity final, vi = velocity initial, tf = time final, ti = time initial)
So if the train's speed went from 25 m/s to 10 m/s, then that means that 10 m/s is our final velocity and 25 m/s is the initial:
a = 10 - 25 / 240
a = -15 / 240
a = -0.0625 m/s^2
Since we ended up with a negative number, it means that the train has a negative acceleration!!!!!
The fast way to do this:
25 m/s is bigger than 10 m/s, so that means that to go from 25 m/s to 10 m/s you have to slow down--otherwise known as putting on your brakes. So if the change in speed is negative then the acceleration will be negative.
In other words, if your final speed is less than your initial speed then your acceleration would be negative.
Sorry for the long explanation! I hope you never struggle with this again though!
Hope it helped,
