Question

The position of a particle moving in a straight line at any time t is x(t) = 2t^2 + 6t + 5. What is the acceleration of the particle at t=3

Answer 1

The acceleration of the particle at any time t

`a = 4\ m/s^(2)`

Explanation:

Given:

The position of a particle moving in a straight line at any time t is.

`x(t) = 2t^(2) + 6t + 5`

The velocity of the particle
`v = (d(x))/(d(t))`

`v = (d)/(d(t))(2t^(2) + 6t + 5)`

`v= 2* 2t + 6`

`v= 4t + 6`

So the velocity of the particle
`v= (4t + 6)\ m/s`

The acceleration of the particle
`a = (d(v))/(d(t))`

`a = (d)/(d(t))(4t + 6)`

`a = 4\ m/s^(2)`

In this condition the acceleration does not depending upon the time, so the acceleration is constant

Therefore the acceleration of the particle at any time t
`a = 4\ m/s^(2)`