An object starts a linear motion with velocity 'u^{prime} and with uniform acceleration ' a^

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7. MOTION

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An object starts a linear motion with velocity $'u^{\prime}$ and with uniform acceleration ' $a^{\prime}$, it acquires a velocity $'v^{\prime}$ in timet

$(a)$ Draw its velocity$-$time graph.

$(b)$ Obtain Ist equation of motion, $v=u+a t,$ for velocity $-$ time relation by using velocity$-$time graph.

$(c)$ A body moving with a velocity of $2\, m s ^{-1}$ acquires a velocity of $10 \,m s ^{-1}$ in $5\, s$. Find its acceleration.

Option A

Option B

Option C

Option D

Solution

$(a)$ The $v-t$ graph is as shown

$(b)$ Now, slope of the $v-t$ graph gives the acceleration of the motion.

$a=\frac{v-u}{t-0}=\frac{v-u}{t}$

Hence, $v=u+a t$

$(c)$ By using velocity – time graph

$u=2 m s ^{-1}, v=10 m s ^{-1}, t=5 s$

Using the expression $v=u+a t,$ we have

$a=\frac{10-2}{5-0}=\frac{8}{5}=1.6 m s ^{-2}$

Standard 9

Science

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