Velocity Time graph question [i'm not getting anywhere]

[Acidvoodoo]

"As a car passes point A on a straight road, it's speed is 10m/s, the car moves with constant acceleration, a m/s/s, along the road for T seconds until it reaches point B, where it's speed is Vm/s.
The car travels at this speed for a further 10 seconds, when it reaches the point C. From C it travels for a further T seconds with constant acceleration 3a m/s/s until it reaches a speed of 20 m/s at the point D."

Sketch the [t,v] graph for the motion, and show that V=12.5

ok, this is the first t,v graph I've drawn, so it could be painfully wrong, which may be my first problem, here it is is paint.

anyway, i don't know whether my graph is correcy, and even if it is, i just can't seem to work it out.
tried some trig, trapezium rule, i just feel i have to many unknowns to work this thing out

any push in the right direction is appreciated

alternate link to my graph thingy

http://pics.bbzzdd.com/users/acidvoodoo/physics.JPG

drag and drop into your browser, or copy and paste, to get it to work :)

 

[Acidvoodoo]

dunno if attachement worked?

realised that t should really be a T, and those T's equal

 

[Doc Al]

Originally posted by Acidvoodoo
...
anyway, i don't know whether my graph is correcy, and even if it is, i just can't seem to work it out.
tried some trig, trapezium rule, i just feel i have to many unknowns to work this thing out

Your graph looks fine. Now write down equations describing how the velocity changes during the accelerated periods. (Use $v_f=v_i+a\Delta t$.) Even though there are three unknowns (a, t, v), if you write down the two equations, you will see that you can easily solve for v.

 

[Acidvoodoo]

thanks very muchfor that tip, i worked it out now, very simple in the end :(

but the next part says "the distance from A to D is 675m, find a and t" [from earlier.

the answers are a=1/8 and t=20. i just can't get to these answers, I've tried writing what i know [s, u, v] and trying to work that out, but it doesn't work. also tried taking away the middle section which is 25m, from 675 to get 650, and then dividing that by a ratio of 3:1, as there is a and a 3a , basically just aimless ideas trying to get to the answers, but I've gone wrong. one more try was to write out the forumlas for the sqaures and triangles areas and making them equal 675, then solving for t, but that didn't work.

any ideas for this one?

 

[Doc Al]

Originally posted by Acidvoodoo
any ideas for this one?

You must be making an error somewhere. The distance equals the area under the graph. Just add up the pieces and solve for T. (The middle section does not equal 25m.)