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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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