A-level mechanics question?

Question

the question goes: a car accelerates uniformly over a straight level road if at point A the car travells at 30m/s and at point B it travells at 60m/s find the velocity the car travells at C which is the midpoint of the line AB

Answer 1

Using one of the laws of motion : v^2 = u^2 + 2as.
Let v = velocity at C and s = AC = CB

From A to C : v^2 = 30^2 + 2as, implies : 2as = v^2 - 30^2
From C to B : 60^2 = v^2 + 2as, implies : 2as = 60^2 - v^2

Therefore, v^2 - 30^2 = 60^2 - v^2
or, 2v^2 = 60^2 - 30^2 = 3600 - 900 = 2700
So, v^2 = 2700/2 = 1350
and, v = sqrt(1350) = 15*sqrt(6)
which is approx. 36.74 m/s.

Edit: Sorry, fixed mistake now.

Answer 2

At the midpoint, assuming uniform acceleration, it will be


(60 + 30) /2 = 45m/s (half way between each) in the direction of B.

Answer 3

v=@t+vo so @t = 60-30 =30
d= 1/2 @ t*t +30t =45 t
so t= d/45
and v= @d/45+vo
@d= 45@t= 45*30
If the distance is d/2
v=@*d/90+vo=45 m/s