GATE (TF) Textile 2011 Question Paper Solution | GATE/2011/TF/47

Question 47 (Textile Engineering & Fibre Science)

The acceleration $(a)$ of a cotton tuft flowing through a duct in a straight line follows the relationship $a=8-\frac{t}{5}$ , where acceleration $(a)$ is in cm/s²and time $(t)$ is in $s$ . The velocity (cm/s) of the tuft when acceleration is zero is

(A)	160
(B)	180
(C)	200
(D)	220

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Given in the question-

Acceleration of cotton tuft(a)= $8-\frac{t}{5}$

Where t is time is second
The velocity of cotton tuft(cm/sec)=?
When accelaration is zero

$a=8-\frac{t}{5}$

$0=8-\frac{t}{5}$

$\frac{t}{5}=8$

t=40 sec

Calculation-

$a=8-\frac{t}{5}$
or
$\frac{d_v}{d_t}=8-\frac {t}{5}$

Integration both side-

$\int \frac{d_v}{d_t}=\int (8-\frac {t}{5}) dt$

$\int \frac{d_v}{d_t}=\int (8-\frac {t}{5}) dt$

$v=8t-\frac{t^2}{2\times 5}$

here,
t=40 sec

$v=8t-\frac{t^2}{2\times 5}$

$v=8 \times 40-\frac{40^2}{10}$

$v=320-\frac{1600}{10}$

v=320-160

Velocity(v)=160 cm/sec (Ans)

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