Question

A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___ m distance.

Answer 1

\[ F_R d = \frac{1}{2} m v^2 \] 

From the above relation, we can derive the ratio of distances \(d_2\) and \(d_1\) by using the velocity ratio squared.

\[ \frac{d_2}{d_1} = \left(\frac{v_2}{v_1}\right)^2 = \left(\frac{1}{3}\right)^2 \]

So, the distance ratio is:

\[ \frac{d_2}{d_1} = \frac{1}{9} \]

Now, to find the distance \(d_2\), we multiply the ratio by \(d_1\):

\[ d_2 = d_1 \times \frac{1}{9} \]

Substituting \(d_1 = 27m\):

\[ d_2 = 27m \times \frac{1}{9} = 3m \]