Question

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Answer 1

Question -

An object is moving with a velocity of 24 km/s and it accelerates at 3 km/s² in the same direction of its initial velocity.

a) Calculate the time in which the object would acquire a velocity double of its initial velocity.

b) How much distance would it travel in this time.

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Answer

Given -

u = 24 km/s

a = 3 km/s²

v = 2u

where

$\longrightarrow$u is initial velocity.

$\longrightarrow$v is final velocity.

$\longrightarrow$a is acceleration.

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To find -

1. Time when the velocity is doubled.

2. Distance travelled.

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Formula used -

$\implies$v = u + at

$\implies$s = ut + 1/2at²

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Solution -

$\bf \blue{u = 24 km/s = </p><p>24 × 60 × 60 = </p><p>86400 km/hr}$

$\bf \blue{a = 3 km/s = 3 × 60 × 60 = 10800 km/hr²}$

As we have to find time when the velocity is doubled , so the final velocity is double of initial velocity.

$\bf \red{v = 2u}$

$\implies$$\bf \pink{v = 2 × 86400}$

$\implies$$\bf \pink{v = 172800 km/hr }$

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By the 1st equation of motion and substituting the value -

$\bf\red{ v = u + at}$

$\implies$$\bf\pink{ 1728000 = 86400 + 10800t}$

$\implies$$\bf \pink{86400 = 10800t }$

$\implies$$\bf \pink{t = 8hr}$

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u = 86400 km/hr

a = 10800 km/hr²

t = 8hr

where

$\longrightarrow$u is initial velocity.

$\longrightarrow$a is acceleration.

$\longrightarrow$t is time taken.

$\bf \red{s = ut + 1/2 at²}$

$\implies$$\bf \pink {s = 86400 × 8 + 1/2 × 10800 × 8 × 8}$

$\implies$$\bf \pink { s = 1036800 km}$

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Thanks

Answer 2

Question -

An object is moving with a velocity of 24 km/s and it accelerates at 3 km/s² in the same direction of its initial velocity.

a) Calculate the time in which the object would acquire a velocity double of its initial velocity.

b) How much distance would it travel in this time.

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Answer

Given -

u = 24 km/s

a = 3 km/s²

v = 2u

where

⟶ u is initial velocity.

⟶ v is final velocity.

⟶ a is acceleration.

━━━━━━━━━━━━━

To find -

1. Time when the velocity is doubled.

2. Distance travelled.

━━━━━━━━━━━━━

Formula used -

⟹ v = u + at

⟹ s = ut + 1/2at²

━━━━━━━━━━━━━

Solution -

$u=24km/s=24×60×60=86400km/hr$

$\bf \blue{a = 3 km/s = 3 × 60 × 60 = 10800 km/hr²}$

As we have to find time when the velocity is doubled , so the final velocity is double of initial velocity.

$\bf \red{v = 2u}$

$⟹ \bf \pink{v = 2 × 86400}$

$⟹ \bf \pink{v = 172800 km/hr }$

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By the 1st equation of motion and substituting the value -

$\bf\red{ v = u + at}$

$⟹ \bf\pink{ 1728000 = 86400 + 10800t}$

$⟹ \bf \pink{86400 = 10800t }$

$⟹ \bf \pink{t = 8hr}$

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u = 86400 km/hr

a = 10800 km/hr²

t = 8hr

where

⟶ u is initial velocity.

⟶ a is acceleration.

⟶ t is time taken.

$s=ut+1/2at²$

$⟹ \bf \pink {s = 86400 × 8 + 1/2 × 10800 × 8 × 8}$

$⟹ \bf \pink { s = 1036800 km}$

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