Question

The position of a particle is given by

x = 3t^3 + t^2 + 5

where x is in m and t in second. Find the acceleration of the particle at t = 2 sec.​

Answer 1

x=3t^3+t^2+5
dx/dt=9t^2+2t = v
dv/dt=18t+2= a
a=18t+2
=18.2+2 (t=2)
=38

Answer 2

Solutio

Acceleration is the rate at which particle of given mass change its velocity.

Velocity is the rate at which particle change its displacement.

Mathematically

Velocity = dx/dt

Acceleration = dv/dt = d²x/dt²

X = 3t³ + t² + 5

dx/dt = 9t² + 2t

d²x/dt² = 18t

acceleration = 18t

Acceleration at t = 2 is 36m/sec²