Question

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Physics :-
A body is moving with a uniform Acceleration and describes 75m in the 6th second and 115m in the 11th second. Show that it moves 115m during the 16th second.

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Answer 1

Question has some error, the correct question is :

Q: A body is moving with a uniform Acceleration and describes 75 m in the 6th second and 115 m in the 11th second. Show that it moves 155 m during the 16th second.

Solution :-

Given : A body is moving with a uniform Acceleration.

Formula used : Sₓ = u + a (n - 1/2)

Here,

Sₓ = Displacement

a = Acceleration

u = Initial velocity

n = n th second

Case I : It moves 75 m in the 6th second.

=> 75 = u + a(6 - 1/2)

=> 75 = u + 11a/2

=> u = 75 - 11a/2 ______(i)

Case II : It moves 115 m in the 11th second.

=> 115 = u + a(11 - 1/2)

=> 115 = u + 21a/2

=> 115 = 75 - 11a/2 + 21a/2 [from equation (i)]

=> 115 = (150 - 11a + 21a)/2

=> 230 = 150 + 10a

=> 230 - 150 = 10a

=> 80/10 = a = 8

Now,

Putting the value of a in equation (i) we get,

=> u = 75 - 11 × 8/2

=> u = 75 - 44 = 31

Now,

S₁₆ = 31 + 8(16 - 1/2)

= 31 + 8 × 31/2

= 31 + 124

= 155

Hence,

It moves 155 m during the 16th second.

Answer 2

$\sf {\underline{\underline{Answer :-}}}$

$\implies$ Let :-

u = Initial velocity

a = Acceleration

$\implies$ Distance travelled in the nth second is given by,

$\sf {S_n = u + {\dfrac {a}{2}}( 2n - 1 )}$

Given : Distance travelled in the 6th second = 75 m

$\sf {\therefore 75 = u + {\dfrac {a}{2}}( 2 \times 6 - 1 )}\\\\\\</p><p></p><p></p><p></p><p>\sf {\implies 75 = u + {\dfrac {11a}{2}}\qquad ..... ( 1 )}$

Given : Distance travelled in the 11th second = 115 m

$\sf {\therefore 115 = u + {\dfrac {a}{2}}( 2 \times 11 - 1 )}\\\\\\</p><p></p><p></p><p></p><p>\sf {\implies 5 = u + {\dfrac {21a}{2}}\qquad ..... ( 2 )}$

Subtracting eq ( 1 ) from ( 2 ), we get :

$\sf {\:115 = \cancel u + {\dfrac {21a}{2}}}</p><p>\\ \sf {( - )75 = \cancel u + {\dfrac {11a}{2}}}$

___________________________________________

$\sf {40 = 5a}\\\\\\</p><p></p><p></p><p>\sf {a = 8 {\dfrac {m}{s^{2}}}}$

Substituting value of a in equation ( 1 ) :

$\sf {\implies 75 = u + {\dfrac {11 \times 8}{2}}}\\\\\\</p><p></p><p></p><p></p><p>\sf {\implies 75 = u + 44}\\\\\\</p><p></p><p></p><p></p><p>\sf {\implies u = 31 {\dfrac {m}{s}}}\\\\\\</p><p></p><p></p><p></p><p>\sf {S_{16} = 31 + {\dfrac {8}{2}}( 2 \times 16 - 1 )}\\\\\\</p><p></p><p></p><p></p><p>\sf {\implies S_{16} = 31 + 4 \times 31}\\\\\\</p><p></p><p></p><p></p><p>\sf {\implies S_ {16} = 155 m}$

•°• Distance travelled in the 16th second = 155 m

$\boxed {\boxed {\sf {Hence \: Proved \:!}}}$