Answer
i) It is possible.
ii) They do not necessarily have the same kinetic energy.
- Object A: $p=12kg.m/s$ and $KE=36J$
- Object B: $p=12kg.m/s$ and $KE=12J$
Work Step by Step
i) We have $p=mv$, so even though 2 objects have different speeds, if they have appropriate masses, their momenta can still have the same amplitude.
ii) We have $p=mv$ and $KE=\frac{1}{2}mv^2=\frac{1}{2}pv$
So if we have 2 objects A and B, where $p_A=p_B$ but $v_A\ne v_B$, then $\frac{1}{2}p_Av_A\ne\frac{1}{2}p_Bv_B$, or $KE_A\ne KE_B$
Therefore, 2 objects with the same momenta do not necessarily have the same kinetic energy.
1) Object A: $m=2kg$ and $v=6m/s$
$p_A=mv=12kg.m/s$
$KE_A=\frac{1}{2}mv^2=36J$
2) Object B: $m=6kg$ and $v=2m/s$
$p_B=mv=12kg.m/s$
$KE_B=\frac{1}{2}mv^2=12J$
