Question 26
In order that a train
can stop safely, it will always pass a signal showing a yellow light before it
reaches a signal showing a red light. Drivers apply the brake at the yellow
light and this results in a uniform deceleration to stop exactly at the red
light.
The distance between
the red and yellow lights is x.
If the speed of the
train is increased by 20%, without changing the deceleration of the train, what
must be the minimum distance between the lights?
A 1.20 x B 1.25
x C 1.44
x D 1.56
x
Reference: Past Exam Paper – November 2010 Paper 11 Q9 & November 2016
Paper 12 Q10
Solution:
Answer:
C.
Since there is a uniform
deceleration, we can use the equations of uniformly accelerated motion.
When the initial speed of
train is u,
Distance between red and
yellow lights = x
Final speed of train = v =
0 [the train stops]
v2 = u2
+2as
0 = u2 + 2ax
u2 ∝ x [The distance
is proportional to the square of the initial speed.]
Now, the initial speed of
the train is increase by 20%.
New speed unew
= 100% + 20% = 120%
New speed unew
= 1.20 u
Since the deceleration is
kept constant, u2 ∝ x
New distance xnew
∝ (unew)2 = (1.20 u)2 = 1.44 u2 = 1.44 x [since u2 ∝ x]
Is this question related to Kinematics topic cause i don't get how u^2 is proportional to x.
ReplyDeleteyes, just follow the derivation above from the equation of motion
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