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2.Motion in Straight Line
hard
The relation between position $( x )$ and time ( $t$ ) are given below for a particle moving along a straight line. Which of the following equation represents uniformly accelerated motion? [where $\alpha$ and $\beta$ are positive constants]
A$\beta x=\alpha t+\alpha \beta$
B$\alpha x=\beta+t$
C$x t=\alpha \beta$
D$\alpha t=\sqrt{\beta+x}$
Solution
(d)
For uniformly accelerated motion,
$v^2=u^2+2 a s$
$\quad \downarrow$
Constant
or
$s=ut+\frac{1}{2} a t^2$
$\quad \downarrow$
Constant
$x=\frac{1}{2} a t^2+u t$
Or the maximum power of $t$ has to be two.
So, $4$.
For uniformly accelerated motion,
$v^2=u^2+2 a s$
$\quad \downarrow$
Constant
or
$s=ut+\frac{1}{2} a t^2$
$\quad \downarrow$
Constant
$x=\frac{1}{2} a t^2+u t$
Or the maximum power of $t$ has to be two.
So, $4$.
Standard 11
Physics
