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2.Motion in Straight Line
medium
The displacement $(x)$ of a particle depends on time $t$ as $x=\alpha t^2-\beta t^3$. Choose the incorrect statements from the following.
A
The particle never returns to its starting point
B
The particle comes to rest after time $\frac{2 \alpha}{3 \beta}$
C
The initial acceleration of the particle is zero
D
$(a)$ and $(c)$ Only
Solution
(d)
$x=0$ at $t=0$ and $t=\alpha / \beta$. So, the particle returns to starting point at $t=\alpha / \beta$
$v=\frac{d x}{d t}=2 \alpha t-3 \beta t^2$
At $t=0, v=0$ i.e. initial velocity of particle is zero.
$v=0$ at $t=0$ and $t=\frac{2 \alpha}{2 \beta}$
Thus, the particle comes to rest after time
$t=2 \alpha / 3 \beta$
$a=\frac{d v}{d t}=2 \alpha-6 \beta t$
At $t=0, a=2 a \neq 0$
Standard 11
Physics
