Answer:
a) [tex]v(t) = 3 \cdot t^{2} - 3\\a(t) = 6 \cdot t[/tex], b) [tex]a(3) = 18\,\frac{m}{s^{2}}[/tex], c) [tex]a(1) = 6\,\frac{m}{s^{2}}[/tex]
Step-by-step explanation:
a) The velocity and acceleration function are obtained by deriving the displacement function once and twice, respectively:
[tex]v(t) = 3 \cdot t^{2} - 3\\a(t) = 6 \cdot t[/tex]
b) The acceleration of the particle at such instant is:
[tex]a(3) = 18\,\frac{m}{s^{2}}[/tex]
c) The time when velocity is zero is:
[tex]3\cdot t^{2} - 3 = 0\\t^{2}-1 = 0\\t^{2}=1\\t = 1[/tex]
The acceleration is:
[tex]a(1) = 6\,\frac{m}{s^{2}}[/tex]
