Question

The equation of motion of a particle is s = t3 − 3t, where s is in meters and t is in seconds. (Assume t ≥ 0.) (a) Find the velocity and acceleration as functions of t. v(t) = a(t) = (b) Find the acceleration after 3 s. m/s2 (c) Find the acceleration when the velocity is 0. m/s2

Answer 1

Answer:

a) $v(t) = 3 \cdot t^{2} - 3\\a(t) = 6 \cdot t$, b) $a(3) = 18\,\frac{m}{s^{2}}$, c) $a(1) = 6\,\frac{m}{s^{2}}$

Step-by-step explanation:

a) The velocity and acceleration function are obtained by deriving the displacement function once and twice, respectively:

$v(t) = 3 \cdot t^{2} - 3\\a(t) = 6 \cdot t$

b) The acceleration of the particle at such instant is:

$a(3) = 18\,\frac{m}{s^{2}}$

c) The time when velocity is zero is:

$3\cdot t^{2} - 3 = 0\\t^{2}-1 = 0\\t^{2}=1\\t = 1$

The acceleration is:

$a(1) = 6\,\frac{m}{s^{2}}$