Question

A particle's acceleration is described by the function ax =(10 −t)m/s2, where t is in s. its initial conditions are x0 =0m and v0x =0m/s at t =0s.

Answer 1

Missing question: "At what time is the velocity again zero?"

Solution:

the acceleration of the particle is
$a_x = (10 -t ) ms^{-2}$
the velocity of the particle is the derivative of the acceleration:
$v_x = (10 t - \frac{1}{2}t^2 + v_0) ms^{-1}$
where $v_0 = 0 m/s$ is the initial velocity, given by the problem.

So, to find when the particle's velocity is again zero, we should just put vx=0 and find t:
$10 t - \frac{1}{2} t^2 = 0$
which has two solutions:
t=0 (beginning of motion)
$t=20 s$
and so, the particle velocity returns to zero after 20 seconds.