Question

the displacement X of a particle is given by X=3-5t+2t²find the velocity at t=2second and acceleration ​

Answer 1

$\bf \LARGE \color{pink}Hola!$

GiveN :

$\sf \mapsto \: displacement \: ( x) = 3 - 5t + 2 {t}^{2}$

To FinD :

$\sf \mapsto \: Velocity \: \: at \: \: \: t \: = 2 \: sec$

SolutioN :

$\sf \mapsto \: x = 3 - 5t + 2 {t}^{2}$

$\implies \sf \: v \: = \frac{dx}{dt} = \frac{d}{dt} (3 - 5t + 2 {t}^{2} )$

$\implies \sf \: v \: = \frac{dx}{dt} = \frac{d}{dt} ( 3) - \frac{d}{dt} (5t) + \frac{d}{dt} (2 {t}^{2} )$

$\implies \sf \: v \: = \frac{dx}{dt} = 0 - 5+ 4t$

$\mapsto \sf \: \: \: \: \underline { Velocity \: \: at \: \: t=2 \: sec}$

$\implies \sf \: v \: = - 5+ 4 \times 2$

$\: \: \: \: \: \: \: \therefore \sf \:{ \underline{ \boxed{ \sf{ v \: = 3}}}}$

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HOPE THIS IS HELPFUL...

Answer 2

Question

the displacement X of a particle is given by X=3-5t+2t²find the velocity at t=2second and acceleration

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Given

time =2seconds

displacement= X=3-5t+2t²

To find

velocity

acceleration

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Solution

▪️In order to find the velocity we will differentiate displacement.

$\to \: X=3-5t+2t² \\ \\ \to \bold{\: v = \frac{dx}{dt} } \\ \\ \to {\: v = \frac{d}{dt} } (3-5t+2t² ) \\ \\ \to \bold \blue{ \: v = - 5 + 4t}$

velocity at 2 second

v= 4t-5

v= 4×2 -5

v= 8-5

$\bold \pink {v = 3 \frac{m}{sec} }$

▪️differentiate velocity to Find accleration:

$\to \bold{ \: a = \frac{dv}{dt} } \\ \\ \to \: a = \frac{d}{dt} (4t - 5) \\ \\ \to\bold \green{ a = 4m/sec²}$

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