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