Determine the velocity and acceleration of a particle:

The motion of a particle is determined by the equation s = t 4  - 3 t 3  + 2 t 2  - 8 , where s is in metres and t in seconds. Determine the velocity & acceleration when t = 2 seconds.

Solution

We have

           s = t ⁴ - 3 t ³ + 2 t ² - 8

        ∴ v = ds/dt = 4 t ³ - 9 t ² + 4 t dt

and

 a = dv/ dt = 12 t ² - 18 t + 4

∴ at t = 2, v₂  = 4 × 2³  - 9 × 2² + 4 × 2

= 32 - 36 + 8

= 4 m / sec²

a₂  = 12 × 2²  - 18 × 2 + 4

= 48 - 36 + 4

= 16 m / sec ²