Chapter 9, Problem 54A

If a car traveling at 60 km/h will skid 20 m when its brakes lock, how far will it skid if it is traveling at 120 km/h when its brakes lock? (This question is typical on some driver’s license exams.)

To determine

The distance travelled by the car if it is skid when it breaks lock.

Answer to Problem 54A

Car skid 80.15 m when its break locks travelling with initial velocity of 120 km/h.

Explanation of Solution

Given:

  $\begin{array}{l}{v}_1\text{= 60 km/h = }\left(\text{60}\right)\frac{{\text{10}}^{\text{3}}\text{m}}{\text{3600}\text{sec}}\text{=}\text{16}\text{.66}\text{m/sec}\hfill \\ s_1\text{= 20m}\hfill \\ v_2\text{= 120 km/h}\text{=}\left(\text{120}\right)\frac{{\text{10}}^{\text{3}}\text{m}}{\text{3600}\text{sec}}\text{=}\text{33}\text{.33}\text{m/sec}\hfill \end{array}$

Formula used:

The kinematics equation is,

  $u^2=v^2+2as$

Where,

u = initial velocity

v = final velocity

a = acceleration of the car

s = displacement

Calculation:

When car travelling with initial velocity of 60 km/h, it will skid 20 m when its breaks lock. Final velocity is zero.

Substituting the given values in equation,

  $\begin{array}{l}\therefore u_1{}^2=v_1{}^2+2a{s}_1\\ \therefore {\left(\text{16}\text{.66}\text{m/s}\right)}^{\text{2}}\text{=}{\left(\text{0}\text{m/s}\right)}^{\text{2}}\text{+}\text{2a}\left(\text{20}\text{m}\right)\\ \therefore a\text{=}\frac{\text{277}\text{.55}}{\text{40}}\\ \therefore a\text{=}\text{6}\text{.93}{\text{m/s}}^{\text{2}}\end{array}$

Similarly, when car travelling with initial velocity of 120 km/h, its breaks lock with final velocity zero.

Considering the deceleration of the car is 6.93 m/s²

Using value in equation,

  $\begin{array}{l}\therefore u_2{}^2=v_2{}^2+2a{s}_2\\ \therefore {\left(\text{33}\text{.33}\text{m/s}\right)}^{\text{2}}\text{=}{\left(\text{0}\text{m/s}\right)}^{\text{2}}\text{+}\text{2}\left(\text{6}\text{.93}{\text{m/s}}^{\text{2}}\right)\left({\text{s}}_{\text{2}}\right)\\ \therefore s_2\text{=}\frac{\text{1110}\text{.88}}{\text{13}\text{.86}}\\ \therefore s_2\text{=}\text{80}\text{.15}\text{m}\end{array}$

Conclusion:

Car skid 80.15 m when its break locks travelling with initial velocity of 120 km/h.