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A particle experiences constant acceleration for $20\ seconds$ after starting from rest. If it travels a distance $D_1$ in the first $10\ seconds$ and distance $D_2$ in the next $10\ seconds$ then:a. $D_2=D_1$b. $D_2=2D_1$c. $D_2=3D_1$d. $D_2=4D_1$
For the first 10 seconds:
Here, initial velocity $u=0$
Time $t=10\ s$
Let $a$ be the constant acceleration.
On using the equation of motion $s=ut+\frac{1}{2}at^2$
$D_1=0+\frac{1}{2}a\times10^2$
Or $D_1=50a$ ....... $(i)$
For next 10 seconds:
velocity after 10 seconds $v=u+at=0+a\times10=10a$
Initial velocity $=10a$
Therefore, $D_2=10a\times10+\frac{1}{2}a\times10^2$
Or $D_2=100a+50a$
Or $D_2=150a$ ....... $(ii)$
On comparing, $(i)$ and $(ii)$
We have $D_2=3D_1$
Therefore, option c. is correct.
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