Question

A car is travelling at a speed of 90 km/h. Brakes are applied so as to produce a uniform acceleration of – 0.5 m/s2. Find how far the car will go before it is brought to rest? options: 8100 m 900 m 625 m 620 m
click pic of solution

Answer 1

GiveN :

• Initial velocity (u) = 90 km/h
• Final velocity (v) = 0 m/s
• Acceleration (a) = - 0.5 m/s²

To FinD :

• Distance travelled by car before coming to rest.

SolutioN :

Convert initial velocity into m/s by multiplying it to 5/18 .

$\implies \rm{u\ =\ 90\ kmh^{-1}} \\ \\ \\ \implies \rm{u\ =\ 90\ \times \: \dfrac{5}{18}} \\ \\ \\ \implies \rm{u\ =\ 25\ ms^{-1}}$

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Now, use 3rd equation of motion :

$\implies \rm{v^2 - u^2 = 2as} \\ \\ \\ \implies \rm{0^2 - 25^2 = 2 \times -0.5 \times s} \\ \\ \\ \implies \rm{0 - 625 = -s} \\ \\ \\ \large \implies {\boxed{\rm{s \: = \: 625 \: m}}} \\ \\ \\ \underline {\rm{\therefore \: Distance \: travelled \: by \: car \: is \: 625 \: m}}$

Answer 2

GivEn:-

• Initial speed of train (u) = 90km/h

• Final speed of train (v) = 0

• Acceleration produced by brakes = -0.5 m/s²

To find:-

• Distance acquired by car.

SoluTion:-

GivEn that,

☯ Initial Speed of Train = 90km/h

$\implies \sf 90 \times \dfrac{5}{18}$ = 25m/s

☯ Final Speed of Train = 0

★ Formula used:-

$\dag\;{\underline{\boxed{\bf{\blue{v = u + at}}}}}$

Here, car will be rest so, Final Velocity = 0

$:\implies\sf 0 = 25 - 0.5t$

$:\implies\sf 0.5t = 25$

$:\implies\sf t = \dfrac{25}{0.5}$

$:\implies{\underline{\boxed{\bf{\pink{t = 50\;sec}}}}}$ ★

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★ Again we use formula,

$\dag\;{\underline{\boxed{\bf{\blue{s = it + \dfrac{1}{2} at^2}}}}}$

$:\implies\sf s = 25 \times 50 + \dfrac{1}{2} 0.5 \times (50)^2$

$:\implies\sf s = 1250 + \dfrac{1}{2} 0.5 \times 2500$

$:\implies\sf s = 1250 - 625$

$:\implies{\underline{\boxed{\bf{\pink{s = 625m}}}}}$ ★

$\dag$ Hence, The car will cover a distance of 625m before coming to rest.

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Additional Information:-

☯ There are three equations of motion:-

★ v = u + at

✩ s = ut + ${}^{\text1}\!/{}_{\text{2}}$at²

★ 2as = v² - u²

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