Question 1

Find the velocity and acceleration if x=t³ +2t²+4 at a time 2s

Question 2

Answer:

$\textsf {v = 20 m/s}$

$\mathsf {a = 16 m/s^2}$

Step-by-step explanation:

$\textsf {To find velocity, let's differentatiate x :}$
$\implies \mathsf {v = (dx)/(dt) }$

⇒
$\mathsf {v = (d)/(dx)(t^(3)+2t^(2)+4) }$

⇒
$\mathsf {v = 3t^(2) +4t +0 }$
$\textsf {(By applying law of differentiation)}$

$\textsf {Substitute t = 2 :}$

⇒
$\mathsf {v = 3(2)^(2) + 4(2) }$

⇒
$\textsf {v = 12 + 8}$

⇒
$\textsf {v = 20 m/s}$

$\textsf {To find acceleration, let's differentatiate v :}$
$\implies \mathsf {a = (dv)/(dt) }$

⇒
$\mathsf {a = (d)/(dx)(3t^(2)+4t) }$

⇒
$\textsf {a = 6t + 4}$

$\textsf {Substitute t = 2 :}$

⇒
$\textsf {a = 6(2) + 4}$

⇒
$\textsf {a = 12 + 4}$

⇒
$\mathsf {a = 16 m/s^2}$

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