Question

the velocity of a particle is given as v(t) = t^3+2t+1. find the acceleration of the particle at time t = 1 sec​

Answer 1

$\large\underline{\underline{\sf Given:}}$

• V(t) = t³ + 2t + 1

• Time (t) = 1 sec

$\large\underline{\underline{\sf To\:Find:}}$

• Acceleration (a) = ?

$\large\underline{\underline{\sf Solution:}}$

As we know ,

$\large\implies{\sf \dfrac{dv}{dt}=a }$

•°•

$\large\implies{\sf \dfrac{dv}{dt}=t^3+2t+1 }$

$\large\implies{\sf \dfrac{dv}{dt}=3t^2+2}$

t = 1 sec (Given)

$\large\implies{\sf \dfrac{dv}{dt}=3×1^2+2 }$

$\large\implies{\sf \dfrac{dv}{dt}=5}$

$\large\implies{\sf a=\dfrac{dv}{dt}=5m/s^2 }$

$\Large\underline{\underline{\sf Answer:}}$

•°• Accleration of the particle is 5m/s²