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Wednesday, January 3, 2018

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.



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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