Answer:
D = 6.74 m
Explanation:
Let the f newtons be the braking force
distance to stop = x meters
speed = v m/s
we know that work done is given as
work done W = fx joules
[tex]fx = \frac{1}{2} mv^2[/tex]
If the speed is doubled ,
[tex]fx' = \frac{1}{2} m(2v)^2[/tex]
[tex] = 4[\frac{1}{2}mv^2] = 4fx[/tex]
stooping distance is D = 4x
[tex]40km/h = \frac{40*1000}{60*60} = 11.11 m/s[/tex]
60 km/hr = 16.66 m/s
braking force = f
[tex]f*3 = [\frac{1}{2}mv^2] = [\frac{1}{2}m*11.11^2][/tex]
[tex]f*D = [\frac{1}{2}m*16.66^2][/tex]
[tex]\frac{D}{3} = \frac{16.66^2}{11.11^2}[/tex]
[tex]\frac{D}{3} = 2.2489[/tex]
D = 6.74 m
