#Velocity time graph help
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iron hare
Here’s my working out but I got 400 instead of 40. I decided to do one thirds of the total area and only looked at the first triangle since it only wants the time of acceleration
Could someone please explain what the mark scheme is doing i dont understand anything from the markscheme lol
royal wave
Here’s my working out but I got 400 instead of 40. I decided to do one thirds of...
What are you trying to find?
iron hare
Oh oops lol sorry i thought i put that into the chat. One sec
Part B
I ended up understanding it though. Split the graph into two triangles and a rectangle. Find the areas of all of them and make an equation
royal wave
Suppose the time spent accelerating is t1 and the time spent decelerating is t2, and the total time is T. Then:
v(t) = ...
...a1 t, 0 ≤ t ≤ t1
...a1 t1, t1 ≤ t ≤ T - t2
a1t1 - a2 (t - t2 + T), T - t2 ≤ t ≤ T
We are also given t2/t1 = k and a1 t1 = v1, so let's rewrite it like this:
v(t) = ...
...v1 t/t1, 0 ≤ t ≤ t1
...v1, t1 ≤ t ≤ T - kt1
v1 - a2 (t - T + kt1), T - kt1 ≤ t ≤ T
As v(T), we get:
v1 - ka2 t1 = 0
a2 = v1/(k t1)
So, for the third piece we get:
v1 - a2 (t - T + kt1) = v1 - v1 (t - T + kt1)/(kt1) = (v1/(kt1))(T - t)
Thus, we get:
v(t) = ...
...v1 t/t1, 0 ≤ t ≤ t1
...v1, t1 ≤ t ≤ T - kt1
(v1/(kt1))(T - t), T - kt1 ≤ t ≤ T
Now the only thing we don't know is t1. To find it, we need to find x(t). Can you do that?
iron hare
what is x(t) ?
royal wave
As usual, position.
iron hare
What sort of position ? As in the starting position ?
iron hare
Oh i don't know anything about that sorry. My school hasn't even started intergration with us yet (i assume integral has something to do with intergration). But i can show you what i did to achieve the answer if you would like
royal wave
Oh i don't know anything about that sorry. My school hasn't even started intergr...
Well, integration in this case is equivalent to finding the area.
Though, if you want to solve generally, you'll have to make a precise graph.
royal wave
Well, I can't check it very quickly, as you didn't solve it generally.
Let me show what it would look like in that case.
iron hare
Alrighty
royal wave
Here you go.
iron hare
Oh alright so the area would be:
1/2 (v1xt1) + v1(T-kta) + 1/2(Txv1) ??
royal wave
Not exactly. More specifically, we get:
x(T) = (1/2)v1 t1 + v1 (T - (k + 1)t1) + (1/2)kv1 t1
From this you can find t1.
iron hare
Ah ok
iron hare
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