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2.Motion in Straight Line
easy
The posttion of an object moving along $x$ -axis ts given by $x=a+b t^{2}$ where $a=8.5\; \mathrm{m}, b=2.5 \;\mathrm{m} \mathrm{s}^{-2}$ and $t$ is measured in seconds. What is the velocity at $t=0\;s$ and $t=2.0 \;s$?
A
$10 \;\mathrm{m} \mathrm{s}^{-1}\;,\;20 \;\mathrm{m} \mathrm{s}^{-1}$
B
$0 \;\mathrm{m} \mathrm{s}^{-1}\;,\;20 \;\mathrm{m} \mathrm{s}^{-1}$
C
$0 \;\mathrm{m} \mathrm{s}^{-1}\;,\;10 \;\mathrm{m} \mathrm{s}^{-1}$
D
$0 \;\mathrm{m} \mathrm{s}^{-1}\;,\;0 \;\mathrm{m} \mathrm{s}^{-1}$
Solution
$v=\frac{\mathrm{d} x}{\mathrm{d} t}=\frac{\mathrm{d}}{\mathrm{d} t}\left(a+b t^{2}\right)=2 b t=5.0 \mathrm{t} \mathrm{m} \mathrm{s}^{-1} $
At $t=0$ s, $\quad v=0 \mathrm{m} \mathrm{s}^{-1}$ and
at $ t=2.0 \mathrm{s}$ $v=10 \mathrm{m} \mathrm{s}^{1}$
Standard 11
Physics
