Question

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

Answer 1

`\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}`