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, v_{2 } = 4 × 2^{3} - 9 × 2^{2 }+ 4 × 2
= 32 - 36 + 8
= 4 m / sec^{2}
a_{2} = 12 × 2^{2} - 18 × 2 + 4
= 48 - 36 + 4
= 16 m / sec ^{2}