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