hmm very nice, you got it correct under the interpretation that it accelerated from rest to 100 km/h and drove at constant speed until decelerating to rest again. However, this isn't the interpretation that was taken by the source of this question and honestly I don't blame you for 'misunderstanding' because it isn't worded very well. Basically, the interpretation aimed by whoever wrote this problem was that the car accelerated at a rate equal to that which requires 3.5 s to reach 100 km/h which it then snaps to decelerating at a scale of 0.7g. It wasn't made clear and but it was supposed to be understood that 100 km/h is NOT the top speed rather the opening sentence was just meant to give you the acceleration in forward motion nothing much more than that:
Here's an image of the solution so u can see what I meant:
View attachment 46732
The main goal here was to find an expression for our desired variable T i.e. minimal time taken, in terms of what variables we know , i.e. distance travelled, acceleration and deceleration. The tricky part here that I was tryna play at you with comes up in the first line involving v, sub, max . Your intuition probably would have been strong enough to deduce this but basically I was trying to play at you with this particular step. See how they used v=u+at, for the acceleration a to equate to v,sub,max but they also got this other equation involving the deceleration where they IMAGINED (srsly how tf were you meant to come up with that) that the car was instead accelerating at the rate 0.7g and from the graph it is evident that'd have taken (T-t,nought, seconds) to have achieved. so v,max, = 0.7g * (T-t,nought,) Combining these two you get an
expression (
THIS IS KEY) for t,nought in terms of acc. deceleration and total time. You then combine this with an expression for the area under the graph D=1 km = 1/2 * base * height = 1/2 * T * v,max, . you then sub in for v,max, (a*t,nought) and then sub in that expression for t,nought, the
key expression which is in terms of acceleration, deceleration and total time. Finally you rearrange to isolate total time, T and finally you plug-in values and then ur DONE.
TL;DR for some it may have been obvious ofc some people have a very strong intuition for these kinda things but 4 yr 11 like myself i thought the trick at the beginning where you have to look at the graph in BOTH directions to make a vital eqn., relating the variables, was a hard to see and thus a challenge. Again if it wasn't a challenge sorry I tried my best.
i got something like this and the equation seems to make sense? btw when i said the force applied to M horizontally should be N i meant only N
