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
Hi. Why did u divide by 1?
ReplyDeleted / 3.6v is the same as (1/3.6) x (d/v)
Deletewhy did you write:
DeleteNew Value of V2=3.6V
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