Question

A jeep travelling with a velocity of 108kmph is brought to rest by applying brakes. It experiences a uniform retardation of 3ms −2. Before coming to rest, it travels a distance of​

Answer 1

$\blue{Given,}$

$\red✇ \green{\: A \: jeep \: travelling \: with \: a \: velocity \: of \: 108 \: km/h }$

$\blue✇ \orange{\: It \: is \: brought \: to \: rest \: by \: applying \: brakes}$

$\pink✇ \red{\: It \: experiences \: a \: uniform \: retardation \: of \: 3m/s² }$

$\blue{To \: Find,}$

$\orange{Distance \: travelled \: by \: Jeep \: before \: coming \: to \: rest}$

$\pink{Converting \: Initial \: Velocity \: in \: m/s }$

$\green{Initial \: Velocity=108 \: km/h }$

$\blue{= (108 \times \frac{5}{18} ) \: m/s}$

$\orange{= ( \frac{540}{18} ) \: m/s}$

$\pink{Initial \: Velocity=30 \: m/s}$

$\red{Calculating \: Required \: Distance,}$

$\pink❍ \blue{ \: Initial \: Velocity = u = 30m/s}$

$\orange❍ \green {\: Final \: Velocity = v = 0m/s}$

$\blue❍ \pink{\: Acceleration = a = - 3 m/ {s}^{2} }$

$\red{Let \: time \: taken \: by \: Jeep \: to \: stop \: be = t \: second}$

$\red★ \blue{\: We \: have \: {1}^{st} \: equation \: of \: motion \: as}$

$\orange{v = u + at}$

$\blue➲ \green{Putting \: values \: in \: {1}^{st} \: equation}$

$\pink{0 = 30 + ( - 3) \times t}$

$\red{ - 3t = - 30}$

$\orange{t = \frac{30}{3} }$

$\green{t = 10s}$

${ \pink {\boxed {\red{t = 10s}}}}$

$\pink★ \green{We \: have \: {2}^{nd} \: equation \: of \: motion \: as}$

$s = \pink{ ut + \frac{1}{2} {at}^{2} }$

$\red➲ \blue{Putting \: values \: in \: {2}^{nd} \: equation}$

$\orange{s = 30 \times 10 + \frac{1}{2} \times ( - 3) \times {10}^{2} }$

$\red{s = 300 - 150}$

${ \green {\boxed {\pink{s = 150m}}}}$

$\blue{ Therefore,}$

$\pink{Distance = 150m}$