What’s the answer to this a level maths question?
A car takes 60 seconds to travel between two sets of traffic lights, starting from rest at the first set and coming to rest again at the second. It accelerates uniformly to a speed of 12m/s and then immediately brakes to reach the second set of lights. Find the distance between the two sets of lights.
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This is the suvat version of Puzzling's answer.
We are given the initial velocity, the fastest velocity, the final velocity and the overall time but we don't know any distances (or the acceleration). From a peruse of the suvat equations this suggests using,
s = 1/2 (u + v)t
and having acceleration over s1 for t1, then braking over s2 for t2, with an overall distance travelled of s = s1 + s2, in a time of t1 + t2 = 60 seconds
s1 = 1/2 (0 + 12) t1
s2 = 1/2 (12 + 0) t2
s1 = 6 t1
s2 = 6 t2
Adding both together (and remembering s1 + s2 = s),
s = 6 t1 + 6 t2
s = 6 (t1 + t2)
s = 6 (60)
s = 360
Draw a graph of the speed vs. time and it will look like a triangle. The base is 60 seconds and the height is 12 m/s.
The area of this triangle represents distance.
A = ½bh
= ½60*12
= 360 m
Answer:
360 m
P.S. Note: You don't even have to know the exact rate of acceleration and deceleration. You might have a gradual acceleration and a rapid deceleration or vice versa, but as long as you know the total time is 60 seconds, you can figure out the distance.