Answer:
Velocity, V = 3t²- 28t+6
Displacement, s = t³ - 14t²+6t -8
At t = 5.8 s
s = -249.05 m
v = -55.48 m/s
At t = 12.7 s
s = -141.48 m
v = 134.27 m/s
Explanation:
We have acceleration of a particle is given by a = 6t - 28
Velocity
At t = 0 we have v₀ = 6 m/s
v₀ = 6 = 3 x 0 ²-28 x 0+C
C = 6
So velocity, V = 3t² - 28t+6
Displacement
At t = 0 we have s₀ = -8 m
s₀ = -8 = 0³ + 14 x 0² + 6 x 0 + C
C = -8
So displacement, s = t³ - 14t²+6t -8
At t = 5.8 s
s = 5.8³ - 14 x 5.8²+6 x 5.8 - 8 = -249.05 m
v = 3 x 5.8² - 28 x 5.8 + 6 = -55.48 m/s
At t = 12.7 s
s = 12.7³ - 14 x 12.7²+6 x 12.7 - 8 = -141.48 m
v = 3 x 12.7² - 28 x 12.7 + 6 = 134.27 m/s