Question

A bus moving with velocity of 72 km/hr after travelling the distance of 200 km driver brought the bus to rest. Calculate the retardation and time taken.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Retardation=0.001\:m/s^{2}}}}$

$\green{\tt{\therefore{Time\:taken=20000\:sec}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial \: speed(u) = 72 \: km/h \\ \\ \tt: \implies Distance \: travel(s) = 200 \: km \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Retardation \: of \: bus = ?$

• According to given question :

$\tt \circ \: Initial \: speed = 72 \times \frac{5}{18} = 20 \: m/s \\ \\ \tt \circ \: Final \: velocity = 0 \: m/s\\ \\ \tt\circ\:Distance=200000\:m\\\\\bold{As \: we \: know \: that} \\ \tt: \implies {v}^{2} = {u}^{2} + 2as \\ \\ \tt: \implies {0}^{2} = {20}^{2} + 2 \times a \times 200000 \\ \\ \tt: \implies 0 = 400 + 400000 \times a \\ \\ \tt: \implies - 400 = 400000 \times a \\ \\ \tt: \implies a = \frac{ - 400}{400000} \\ \\ \green{\tt: \implies a = -0.001\: {m/s}^{2} } \\ \\ \green{\tt \therefore Retardation \: of \: bus \: is \: 0.001\: {m/s}^{2} }\\\\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 0 = 20 + ( - 0.001) \times t \\ \\ \tt: \implies - 20 = - 0.001 \times t \\ \\ \tt: \implies t = \frac{ - 20}{ - 0.001} \\ \\ \green{\tt: \implies t = 20000 \: sec}$

Answer 2

Given :

• Initial velocity (u) = 72 kmh¯¹
• Final velocity (v) = 0 kmh¯¹
• Distance travelled (s) = 200 km

To Find :

• Retardation of the bus
• Time taken by the bus

Formulae used :

$v = u + at$

$s = ut + \frac{1}{2} a {t}^{2}$

$2as = {v}^{2} - {u}^{2}$

Solution :

According to the question,

$2as = {v}^{2} - {u}^{2} \\ 2a \times 200 = {0}^{2} - {72}^{2} \\ 2a \times200 = - 5184 \\ 2a = - \frac{5184}{200} \\ a = - \frac{5184}{200 \times 2} \\ a = - 12.96 \: m {s}^{ - 2}$

And,

$v = u + at \\ 0 = 72 - 12.96 \times t \\ 12.96 \times t = 72 \\ t = 0.18 \: sec$

Therefore, the retardation of the bus is 12.96 ms¯² and the time taken is 0.18 seconds.