## Determine the velocity and acceleration of a particle, Mechanical Engineering

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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

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