Question

${\huge{\underline{\underline{\mathfrak{\red{Question:-}}}}}}$
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Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity (v0) and the braking capacity, or deceleration, ?a that is caused by the braking. A car travelling at speed 72km/hr suddenly applies the brake with the deceleration of 5m/s2. Find the stopping distance of the car.
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don't copy :) ​

Answer 1

GIVEN:-

• $\rm{Initial\:Velocity=72km/hr=20m/s}$

• $\rm{Final\:Velocity=0m/s}$(as it will come to rest)

• $\rm{Declaration=5m/s^2}$

TO FIND

• The stopping Distance of the car i.e the distance covered by the Vehicle after the brakes applied.

FORMULAE USED

• ${\boxed{\rm{v^{2}-u^{2}=2as}}}$

Where,

V= Final Velocity

u= Initial Velocity

a= Declaration

s= Distance.

Now,

$\implies\rm{v^2-u^2=2as}$

$\implies\rm{(0)^2-(20)^2=2\times{-5}\times{s}}$

$\implies\rm{-400=-10s}$

$\implies\rm{S=\dfrac{\cancel{400}}{\cancel{10}}}$

$\implies\rm{S=40m}$

Thus, The Distance Travelled by the vehicle is 40m

$\bigstar\rm\blue{Useful\:Equation}\bigstar$

• ${\boxed{\rm{V=u+at}}}$
• ${\boxed{\rm{s=ut+\dfrac{1}{2}\times{a}\times{(t)}^2}}}$.

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{ANSWER}}}}⋆$

• 40 m.

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{EXPLANATION}}}}⋆$

$\blue{\bold{\underline{\underline{Given}}}}$

• Initial Velocity = 72 km/hr = 20 m/s.
• Final Velocity = 0 m/s.
• Declaration = 5 m/s².

$\blue{\bold{\underline{\underline{To \: Find}}}}$

• The stopping distance of the car.

$\blue{\bold{\underline{\underline{Formula}}}}$

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

Where,

† v = Final Velocity

† u = Initial Velocity

† a = Declaration

† s = Distance

$\blue{\bold{\underline{\underline{Solution}}}}$

$\implies\rm{v^2-u^2=2as}$

$\implies\rm{ {(0)}^{2} - {(20)}^{2} = 2 \times - 5 \times s }$

$\implies\rm{ - 400 = - 10s}$

$\implies\rm{S = \dfrac{\cancel{400}}{\cancel{10}}}$

$\implies\rm{s = 40 \: m}$

$\blue{\bold{\underline{\underline{ANSWER}}}}$

• The stopping distance of the car is 40 m.