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Tuesday, January 9, 2018

When a constant braking force is applied to a vehicle moving at speed v, the distance d moved by the vehicle in coming to rest is given by the expression d = kv2



Question 3
When a constant braking force is applied to a vehicle moving at speed v, the distance d moved by the vehicle in coming to rest is given by the expression
d = kv2
where k is a constant.

When d is measured in metres and v is measured in metres per second, the constant has a value of k1.

What is the value of the constant when the distance is measured in metres, and the speed is measured in kilometres per hour?

A 0.0772 k1                       B 0.278 k1                         C 3.60 k1                            D 13.0 k1





Reference: Past Exam Paper – June 2015 Paper 11 Q3





Solution:
Answer: A.

d = kv2

When speed v is in ‘m/s’ and distance d is in ‘m’, the value of k is ‘k1’.
k1 = d / v2


We want to know the value of k when v is in ‘km/h’ and d in ‘m’.

Converting m/s to km/h
1 m/s means that in 1s - - -> 1m
1 h = 3600 s
1s - - -> 1m
1h - - > 3600 m = 3.6 km

Thus, 1 m/.s is equal to 3.6 km/h. Let the new value of speed = v2.
v2 = 3.6 v


New value of k = d / v22 = d / (3.6v)2 = (1 / 3.62) (d / v2)

But d / v2 = k1  

New value of k = (1 / 3.62) k1 = 0.0772 k1

4 comments:

  1. Replies
    1. d / 3.6v is the same as (1/3.6) x (d/v)

      Delete
    2. why did you write:
      New Value of V2=3.6V

      Delete
    3. this is the value of v in km/h. we call it v2 here so that we do not confuse with the original value of v

      Delete

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