Question 7
A bicycle brakes so that
it undergoes uniform deceleration from a speed of 8 m s-1 to 6 m s-1 over
a distance of 7 m.
If the deceleration of
the bicycle remains constant, what further distance will it travel before
coming to rest?
A 7 m B 9 m C 16 m D 21 m
Reference: Past Exam Paper – November 2012 Paper 13 Q8
Solution:
Answer: B.
Since the deceleration is
uniform, we may use the equations of uniformly accelerated motion.
We want to find the further
distance travelled before coming to rest.
Initial speed u = 6 m s-1
Final speed v = 0 m s-1
Distance travelled = s =
???
Let the acceleration = a
(this will be negative since there is a deceleration)
v2 = u2
+ 2as
We need to find ‘a’ first
in order the obtain the further distance travelled ‘s’.
Consider the first part of
the motion.
Final speed v = 6 m s-1
Initial speed u = 8
m s-1
Distance
travelled = 7 m
v2 = u2
+ 2as
Acceleration a = (62
– 82) / (2×7) = - 2 m s-2
Now, consider the second
part of the motion again.
v2 = u2
+ 2as
Distance travelled s = (02
– 62) / (2 × -2) = 9 m
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