Question

HEY MATES I need ......


both if the questions to be solved

plzzzz. :-)

Answer 1

$<b><u><i>Heya mate!!! Here's your solution</i></u>$
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$\huge{\mathcal{(1)}}$
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$\huge{Given}$

The brakes applied to a car produces an acceleration of 10 m/s² in opposite direction of motion. It takes 5 seconds for the car to stop after the application of brakes, then it comes to rest.

$\huge{To\: find}$

The distance covered by the car in the period between application of brakes and car coming to rest.

$\huge{Solution}$

Firstly,

Final velocity of car (v) = 0 m/s (as it comes to rest)

Time taken (t) = 5 sec

Acceleration (a) = -10 m/s² (negative sign because it is deacclerating)
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Let the initial velocity be 'u'

Then, using the first equation of motion, we get,

v = u + at

=> 0 = u + (-10 × 5)

=> 0 = u + (-50)

=> 50 = u

Hence, the initial velocity of the car is 50 m/s.
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Now, let the distance covered be 's'.

Then, using the second equation of motion, we get,

s = ut + ½ at²

=> s = (50×5) + (½ × -10 × 5²)

=> s = (250) + (½ × -10 × 25)

=> s = 250 + ( -5 × 25)

=> s = 250 + (-125)

=> s = 250 - 125

=> s = 125

Hence, the distance covered by the car in this period is 125 m.
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$\huge{\mathcal{(2)}}$
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$\huge{Given}$

The linear speed of the seconds hand of a wall clock is 1.05 cm/s.

$\huge{To \: find}$

The length of the seconds hand.

$\huge{Solution}$

Firstly,

The speed (v) of the seconds hand = 1.05 cm/s

Time taken (t) by the second hand = 1 sec

Therefore,

Distance covered (s) by seconds hand in 1 sec

= v × t
= 1.05 × 1
= 1.05 cm
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Now, 1 min = 60 sec

Hence, distance covered by seconds hand in 60 sec

= 1.05 × 60
= 63 cm
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Here, let the clock be the circle and seconds hand be the radius(r).

Now, the seconds hand completes one revolution in 1 min. So, 63 cm is also the circumference of the circular clock.

But, circumference of any circle
= 2πr

Therefore, both are equal.

=> 2πr = 63

=> 2 × 22/7 × r = 63

=> 44r/7 = 63

=> 44r = 63×7

=> 44r = 441

=> r = 441/44

=> r = 10.03 (approx)

Hence, the length of the seconds hand = 10.03 cm
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$\mathcal{\purple{Finally,}}$

Your answers are -

$\boxed{\bold{\mathcal{\red{(1) \: =\: 125\: m}}}}$
$\boxed{\bold{\mathcal{\pink{(2)\: =\: 10.03\: cm}}}}$
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$\huge{\bold{\mathfrak{\blue{Thank\: you}}}}$