Acceleration-time graph for a particle moving along x -axis is shown in figure. If initial velocity

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2.Motion in Straight Line

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The acceleration-time graph for a particle moving along $x$-axis is shown in figure. If the initial velocity of particle is $-5 \,m / s$, the velocity at $t=8 \,s$ is ....... $m / s$

A

$+15$

B

$+20$

C

$-15$

D

$-20$

Solution

(a)

The area under $a-t$ graph gives change in velocity.

Given, $u=-5 \,m / s$

$\Rightarrow$ Area on positive side $=\frac{1}{2} \times 6 \times 10=30 \,ms ^{-1}$

$\Rightarrow$ Area on negative side $=\frac{1}{2} \times 2 \times 10=10 \,ms ^{-1}$

Net area $=30-10=20 \,ms ^{-1}$

$\Delta v=$ Area

$v-(-5)=20$

$\Rightarrow v=15 \,ms ^{-1}$

Standard 11

Physics

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