Question

The equation of motion of a particle is s = 2t3 − 8t2 + 4t + 2, where s is in meters and t is in seconds. (assume t ≥ 0.) (a) find the velocity and acceleration as functions of t.

Answer 1

The equation of motion of a particle is given by,

s =
`2t^(3) - 8t^(2) + 4t +2`

Let velocity of particle is denoted by v.

The velocity of the particle is given by,

velocity (v) =
`(ds)/(dt)`

v =
`(d)/(dt) [ 2t^(3) - 8t^(2) + 4t +2 ]`

v =
`(d)/(dt) 2t^(3) - (d)/(dt) 8t^(2) + (d)/(dt) 4t + (d)/(dt) 2`

v =
`6t^(2) -16t +4`

Thus, Velocity of particle is given by,

v =
`6t^(2) -16t +4`

Let acceleration of the particle is denoted by a.

The acceleration of particle is given by,

Acceleration =
`(dv)/(dt)`

a =
`(d)/(dt) [6t^(2) -16t +4]`

a =
`(d)/(dt) 6t^(2) -(d)/(dt)16t +(d)/(dt)4`

a = 12t - 16

Thus, acceleration of the particle is given by,

a = 12t - 16