There are two ways of finding the gradient of an exponential of the form y = ae^kx, one is ake^kx, the other is just ky. Since the initial gradient is 15, y must be 75 when t is 0 (I ignored the 25 for this part, I'm not sure whether I should have or not) so 75k = 15 and k = 0.2.
There are two ways of finding the gradient of an exponential of the form y = ae^kx, one is ake^kx, the other is just ky. Since the initial gradient is 15, y must be 75 when t is 0 (I ignored the 25 for this part, I'm not sure whether I should have or not) so 75k = 15 and k = 0.2.
The exponential is decreasing so the power has to be negative. I think the minus was already in the equation they gave us so if k is negative, the power becomes positive because you get -(-0.2) = 0.2 but if k is 0.2 you get -(0.2) = -0.2. I completely forgot about that though so I think I was a bit lucky there.
I can't even remember the equations anymore but instead of doing ky I just compared by doing T(1), little marks anyway so it won't be that deep.
Ah right. The question I thought was a bit weird was the pulleys one. It asked for the distance travelled by the 3kg mass before the string would be taut again. I thought the answer was twice the distance the mass went up since it had to come back down to the same place for the string to be taut again right? So I multiplied my answer by two.
Ah right. The question I thought was a bit weird was the pulleys one. It asked for the distance travelled by the 3kg mass before the string would be taut again. I thought the answer was twice the distance the mass went up since it had to come back down to the same place for the string to be taut again right? So I multiplied my answer by two.
Yeah, I had similar thoughts to you on that one, the first part was light work but I wasn't too sure what it was trying to ask in the second part? I just did something like that to get some sort of legible answer. Anyway the kinematics question last was very nice, almost as nice as the 9 mark integration Q tbh.
Yeah, I had similar thoughts to you on that one, the first part was light work but I wasn't too sure what it was trying to ask in the second part? I just did something like that to get some sort of legible answer. Anyway the kinematics question last was very nice, almost as nice as the 9 mark integration Q tbh.
Not as nice as the seven mark dimensional analysis question where everything equals 1 yesterday though haha. (assuming you do further mechanics and not one of the other modules)
Not as nice as the seven mark dimensional analysis question where everything equals 1 yesterday though haha. (assuming you do further mechanics and not one of the other modules)
That Further Mechanics exam was quite slick actually, I clocked it was a SUVAT equation early on and just wrote it all down, lmao in the follow up question i just wrote k = 1/2 as soon as.
Also what did everyone get as the value of a for the last are under a curve question? I did all the working and ended up with a quadratic in disguise but then I kept getting a value of a which was lower than 8?
Yes, I got a quadratic too but rejected the one that was less than 8 (I think it was -2) and it left me with a = 27. I used the integral function on my calculator to sub it in and check and it was definitely right.
Also what did everyone get as the value of a for the last are under a curve question? I did all the working and ended up with a quadratic in disguise but then I kept getting a value of a which was lower than 8?
how did you get that? Any chance you remember the method?
You are given a lower bound. You are given the function. You are given the area beneath the curve between the lower bound and a. You do what you would normally do with definite integrals, but doing it algebraically. You get a disguised quadratic in a^3/2 or something, you find two roots, you are told that a > 8, so reject the root does not give you a value of a above 8, the other value of a is 27, simple.