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2.Motion in Straight Line
easy
The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 - {e^{ - bt}}]$. Then the velocity of the particle is
A
$k\,({e^{ - bt}})$
B
$\frac{k}{{{b^2}{e^{ - bt}}}}$
C
$k\,b\,{e^{ - bt}}$
D
None of these
Solution
(a) $v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}\left[ {\frac{k}{b}\left( {1 – {e^{ – bt}}} \right)} \right]$$ = \frac{k}{b}\left[ {0 – ( – b){e^{ – bt}}} \right]$$ = k{e^{ – bt}}$.
Standard 11
Physics
