Following is known:
vInitial = 0 mm/s,
vFinal = 100 mm/s,
totalTime = 0.9 sec,
TotalDistance = 100 mm
How can I calculate the maximum velocity that will be reached, considering constant acceleration and deceleration (acc = -decc).
Edit:
I was able to get equation with the help of answer from @Souparna I am providing the equations, for future use if someone has the same query
At $t_1$, $v_{max}$ is achieved.
At $t=0.9 $, $v_f$ is achieved. $$v_{max}=at_1$$ $$v_f=v_{max}-a(0.9-t_1)$$ $$s=\dfrac{1}{2}at_1^2+(0.9-t_1)v_{max}-\dfrac{1}{2}a(0.9-t_1)^2$$ From these we can get, $$v_f=100=at_1-a(0.9-t_1)\implies a=\dfrac{100}{2t_1-0.9}$$ $$s=100=\dfrac{1}{2}at_1^2+(0.9-t_1)at_1-\dfrac{1}{2}a(0.9-t_1)^2$$ Hence,$$100=\dfrac{50t_1^2}{2t_1-0.9}+\dfrac{100t_1(0.9-t_1)}{2t_1-0.9}+\dfrac{50(0.9-t_1)^2}{2t_1-0.9}$$ Solving we get $t_1=\dfrac{1}{20}(\sqrt{202}-2)\approx 0.61063$.
Hence, $a\approx 311.2675$ and $v_{max}\approx 190.0703$.