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2.Motion in Straight Line
hard
Give example of a motion where $x > 0$, $v < 0$, $a > 0$ at a particular instant.
Option A
Option B
Option C
Option D
Solution
Let the motion is represented by
$x(t)=4+5 \mathrm{e}^{-\gamma t}$
Let $A>B$ and $\gamma>0$
Now velocity $x(t)=\frac{d x}{d t}=-5(7) e^{-7 t}$
Acceleration $a(t)=\frac{d x}{d t}=5(7)^{2} e^{-7 t}$
Suppose we are considering any instant $t$, then from Eq. (i), we can say that $x(t)>0 ; v(t)<0$ and $a>0$
$x(t)=4+5 \mathrm{e}^{-\gamma t}$
Let $A>B$ and $\gamma>0$
Now velocity $x(t)=\frac{d x}{d t}=-5(7) e^{-7 t}$
Acceleration $a(t)=\frac{d x}{d t}=5(7)^{2} e^{-7 t}$
Suppose we are considering any instant $t$, then from Eq. (i), we can say that $x(t)>0 ; v(t)<0$ and $a>0$
Standard 11
Physics
