Question

the position of a particle moving along a stright line is given by x=4t-3t^2m find accelaration of the particle at t=2 seconds​

Answer 1

Given :

➳ Position equation of a moving particle has been provided.

$\bigstar\:\boxed{\bf{x=4t-3t^2}}$

To Find :

➳ Acceleration of particle at t = 2s.

SoluTion :

✴ Instananeous velocity :

$\implies\sf\:a=\dfrac{dx}{dt}$

$\implies\sf\:a=\dfrac{d{(4t-3t^2)}}{dt}$

$\implies\bf\:v=4-6t$

✴ Instantaneous acceleration :

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

$\implies\sf\:a=\dfrac{d(4-6t)}{dt}$

$\implies\boxed{\bf{a=-6\:ms^{-2}}}$

⇒ It shows that, Acceleration has constant value throughout the motion. Acceleration doesn't depend on time.

⇒ Magnitude of acceleration at any instant of journey = -6 m/s²