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2.Motion in Straight Line
hard
Equation of motion of a body is $\frac{d v}{d t}=-4 v+8$, where $v$ is the velocity in $m / s$ and $t$ is the time in second. Initial velocity of the particle was zero. Then,
A
the initial rate of change of acceleration of the particle is $8\,m / s ^3$
B
the terminal speed is $2\,m / s$
C
Both $(a)$ and $(b)$ are correct
D
Both $(a)$ and $(b)$ are wrong
Solution
(b)
$a=\frac{d v}{d t}=-4 v+8$
$\therefore \quad \frac{d a}{d t}=-4 \cdot \frac{d v}{d t}=-(-4 v+8)$
$=16 v-32$
$\left(\frac{d a}{d t}\right)_{t=0}=-32\,m / s ^3$
At terminal velocity $a=0$
$\therefore \quad v=2\,m / s$
Standard 11
Physics
