Aparticle starts from rest at a fixed point 0 and its acceleration is 12t^2-24t+8 m/s^2. show that the particle is again at rest when it returns to 0 and find its maxi- mum displacement from 0 before it returns. inte

a) V(2) = 0 The particle is at rest

b) The maximum displacement is 1m

Step-by-step explanation:

Let's first find velocity and displacement from the given acceleration:

Now we need the instant t1 where x(t1) = 0 and then we evaluate v(t1) to find its velcity and verify if it is 0:

Solving for t, we get:

t1 = 0   and t1 = 2s   Now we evaluate v(2):

v(2) = 0m/s  It is at rest when it returns to x=0m

Now, for maximum displacement, we need the instant when v(tm) = 0

 Solving for tm:

tm=0;  tm = 1  and tm = 2

Since x(0) and x(2) are both 0, we calculate x(1) to find the maximum displacement:

x(1) = 1m