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2.Motion in Straight Line
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The velocity $v$ of a body moving along a straight line varies with time $t$ as $v=2 t^2 e^{-t}$, where $v$ is in $m / s$ and $t$ is in second. The acceleration of body is zero at $t=$
A
$0$
B
$2$
C
$3$
D
Both $(a)$ and $(b)$
Solution
(b)
$v=2 t^2 e ^{-t}$
$\frac{d v}{d t}=2\left[t^2 e^{-t} \times(-1)+e^{-t} \times 2 t\right]$
Put, $a=0$,
$-2 t^2 e^{-t}+4 t e^{-t}=0$
$\Rightarrow-2 t^2+4 t=0 \Rightarrow t^2=2 t \Rightarrow t=2 s$
Standard 11
Physics
Similar Questions
Refer to the graph in figure. Match the following
| Graph | Characteristics |
| $(A)$ | $(i)$ has $v > 0$ and $a < 0$ throughout |
| $(B)$ | $(ii)$ has $x > 0,$ throughout and has a point with $v = 0$ and a point with $a = 0$ |
| $(C)$ | $(iii)$ has a point with zero displacement for $t > 0$ |
| $(D)$ | $(iv)$ has $v < 0$ and $a > 0$ |
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