Question

solve plzzzz........​

Answer 1

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) If s = 3t² + 4t + 9 , find

(i) velocity at t = 2s

(ii) average velocity between 1 & 4 second .

${\huge{\underbrace{\rm{Answer\checkmark}}}}$

$\boxed{ \sf \: s = 3 {t}^{2} + 4t + 9 \: }$

As you can see , we have the Equation of distance .

(i) Velocity at t = 2s

We know that ,

Velocity = Rate of change of distance w.r.t. time .

So ,

$\rm \: velocity _{inst} = \frac{ds}{dt}$

$\mapsto \rm \: v _{inst} = \frac{d(3 {t}^{2} + 4t + 9)}{dt}$

$\mapsto \rm \: v _{inst} = \frac{d(3 {t}^{2}) }{dt} + \frac{d(4t)}{dt} + \frac{d(9)}{dt}$

$\mapsto \rm \: v _{inst} = 6t + 4 + 0$

$\leadsto \underline{\underline{\rm \: v _ {inst} = 6t + 4 \: }}$

Now , as we are supposed to find velocity at time = 2 sec .

put it in the above equation ..

$\mapsto \rm \: v _{2 \: sec} = 6(2) + 4 \: \frac{m}{ {s}}$

$\mapsto \rm \: v _{2 \: sec} = 12 + 4 \: \frac{m}{ {s} }$

$\longrightarrow \pink{\boxed{ \rm \: v _{2 \: sec} = 16 \: \frac{m}{s} }}$

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(ii) Average Velocity between 1 & 4 sec .

we have

$\sf \: t _{1} = 1 \: sec$

$\sf \: t _{2} = 4 \: sec$

So , Finding the position of the particle at the respective times .

At t = 1 ,

$\mapsto \rm \: s _{1} = 3 {(1)}^{2} + 4(1) + 9$

$\mapsto \rm \: s_{1} = 3 + 4 + 9 \: m$

$\leadsto \underline{\underline{\rm \: s _{1} = 16 \: m \: }}$

At t = 4 ,

$\mapsto \rm \: s _{2} = 3 {(4)}^{2} + 4(4) + 9$

$\mapsto \rm \: s _{2} = 3 \times 16 + 16 + 9 \: m$

$\mapsto \rm \: s _{2} = 48 + 25 \: m$

$\leadsto \rm \underline{ \underline{ \: s _{2} = 73m \: }}$

Now , using the Formula ↓↓

$\boxed{ \sf \: average \: velocity = \frac{ \triangle{x}}{ \triangle{t}} }$

here ,

∆x = change in position . &

∆t = change in time .

$\mapsto \rm \: average \: velocity = \frac{s _{2} - s _{1} }{t _{2} - t _{1} }$

$\mapsto \rm \: average \: velocity = \frac{73 - 16}{4 - 1} \frac{m}{s}$

$\mapsto \rm \: average \: velocity = \cancel \frac{57}{3} \: \frac{m}{s}$

$\longrightarrow \purple{\boxed{ \rm \: average \: velocity = 19 \: \frac{m}{s} }}$

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So , Final answer :-

16 m/s

19 m/s

• The unit of velocity is always in m/s ( meter per second )