First slide

Rectilinear Motion

Question

A truck is moving at a speed of 72 kmh^-1 on a straight road. The driver can produce deceleration of 2 ms^-2 by applying brakes. The stopping distance of truck is 13x m, if the reaction time of the driver is 0.2 s. The value of x is _________.

Moderate

Solution

$\begin{array}{l} \begin{array}{ll} ∵ & v^{2} = u^{2} + 2 a s \\ \Rightarrow & 0^{2} = {(72 \times \frac{5}{18})}^{2} - 2 \times 2 s_{0} \\ ∴ & s_{0} = \frac{400}{4} = 100 m \end{array} \\ Thus, stopping distance = (72 \times \frac{5}{18}) \times 0.2 + s_{0} \\ = 4 + 100 = 104 = 13 x \\ ∴ x = \frac{104}{13} = 8 \end{array}$

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