A bus moving along a straight highway with speed of $72 \mathrm{~km} / \mathrm{h}$ is brought to halt within $4 s$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ $m$.

<p>A bus traveling along a straight highway at a speed of 72 km/h comes to a stop within 4 seconds after the brakes are applied. To find the distance the bus travels during this time (assuming uniform deceleration), follow these steps:</p> <p>First, convert the initial speed from km/h to m/s:</p> <p> <p>$$\begin{aligned} u &= 72 \times \frac{5}{18} = 20 \, \text{m/s} \end{aligned}$$</p> </p> <p>Given: <br> <p>Initial speed ($ u $) = 20 m/s <br></p> <p>Final speed ($ v $) = 0 m/s <br></p> <p>Time ($ t $) = 4 s </p></p> <p>Using the first equation of motion:</p> <p> <p>$$\begin{aligned} v &= u + at \\ 0 &= 20 + 4a \\ a &= -5 \, \text{m/s}^2 \end{aligned}$$</p> </p> <p>Now, use the second equation of motion to find the distance traveled ($ S $):</p> <p> <p>$$\begin{aligned} S &= ut + \frac{1}{2}at^2 \\ S &= 20 \times 4 + \frac{1}{2} \times (-5) \times 4^2 \\ S &= 80 - 40 \\ S &= 40 \, \text{m} \end{aligned}$$</p> </p> <p>Therefore, the distance traveled by the bus during the time the brakes are applied is 40 meters.</p>