Question

car travels 60 km/h will skid 30 m when its brakes are locked. if the same car is traveling 180 km/h, what will be the skidding distance?

Answer 1

270 m

Step-by-step explanation:

When the driver hits the brakes, the kinetic energy of the car is converted by friction into heat. The kinetic energy K is given by:

(1)
`K=(1)/(2) mv^(2)`

The work W done by friction is:

(2)
`W = F_fd`

where the force of friction is:

`F_f = \mu mg`

d: distance sliding

μ: friction coefficient

m: mass

g: gravitational constant

setting equation 1 and 2 equal:

(3)
`(1)/(2)mv^(2)=\mu mgd`

simplifying:

(4)
`d = (v^(2) )/(2\mu g)`

Use equation 4 to find the ratio between the two cases gives:

(5)
`(d_1)/(d_2) = (v_1^(2) )/(v_2^(2) )`

plugging in:

`(30)/(d_2)=(60^(2) )/(180^(2))`

`d_2=270`