Question

a moving train is brought to rest within 20sec by applying brakes find the initial velocity if the retardation due to brakes is 2m/s²
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Answer 1

Answer

☞ Initial Velocity of the body is 40 m/s

Given

✭ Final Velocity = 0 m/s

✭ Time = 20 sec

✭ Acceleration = -2 m/s²

To Find

✭ Initial Velocity of the body?

Solution

So we shall here use the first equation of motion, that is,

$\underline{\boxed{\tt v = u+at}}$

• u = Initial Velocity
• v = Final Velocity
• a = acceleration (here retardation because it is in the opposite direction to the motion)
• t = Time

Substituting the values,

$\tt :\implies v = u+at$

$\tt :\implies 0 = u+(-2)\times 20$

$\tt :\implies -u = -40$

$\tt :\implies\orange{u = 40 \ m/s}$

»» Velocity is equal to the quotient of the displacement by the time taken

»» It is a vector quantity,i.e it has both Magnitude & Direction

»» V = Displacement/Time

»» SI unit of acceleration is m/s

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☯ $\underline{\boldsymbol{Know \ More}}$

⪼ s = ut+½at²

⪼ v²-u² = 2as

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Answer 2

Given :-

• A moving train is brought to rest within 20 s by applying brakes
• The retardation due to brakes is 2ms²

To Find :-

• Initial velocity

Solution :-

We have,

• Final Velocity(v) = 0 m/s
• Time taken(t) = 20 s
• Acceleration(a) = - 2 m/s

We know that,

$\boxed{\sf v = u + at}$

Where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time taken

Substituting the give values we get,

$:\implies\sf0 = u + (- 2) \times 20$

$:\implies\sf\cancel- u = \cancel- 40$

$:\implies\underline{\boxed{\blue{\bf u = 40 \: m/s}}}$

$\green{\therefore\sf Initial\:Velocity\:of\:the\:body\:is\:40\:m/s}$

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Additional Information :-

★ 2nd equation of motion :-

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

Where,

• s = Distance Covered
• u = Initial Velocity
• t = Time taken

★ 3rd equation of motion :-

$\boxed{\sf v^{2} - u^{2} = 2as}$

Where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• s = Distance Covered

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