The units for the rate constant and the rate of reaction are same for a reaction. What will be the order of the reaction?

The rate for the reaction $A + B \rightarrow \text{product}$ is $1.8 \times 10^{-2} \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the reaction is second order in $A$ and first order in $B$,given $[A] = 0.2 \ M$ and $[B] = 0.1 \ M$.

Which is the unit of the rate constant for a second-order reaction?

The reaction $CH_{3}COF + H_{2}O \rightleftharpoons CH_{3}COOH + HF$ is studied under two conditions:
Condition $I$: $[H_{2}O]_{0} = 1.00 \ M$,$[CH_{3}COF]_{0} = 0.01 \ M$
Condition $II$: $[H_{2}O]_{0} = 0.02 \ M$,$[CH_{3}COF]_{0} = 0.80 \ M$

Time $(t)$ min (Condition $I$) / $[CH_{3}COF]$ $M$	Time $(t)$ min (Condition $II$) / $[H_{2}O]$ $M$
$0$ / $0.01000$	$0$ / $0.0200$
$10$ / $0.00867$	$10$ / $0.0176$
$20$ / $0.00735$	$20$ / $0.0156$
$40$ / $0.00540$	$40$ / $0.0122$

Determine the overall order of the reaction and calculate the rate constant.

For a reaction $2 \ A + B \rightarrow P$, when the concentration of $B$ alone is doubled, the rate does not change, and when the concentrations of both $A$ and $B$ are doubled, the rate increases by a factor of $4$. The unit of the rate constant is,

For a given reaction $t_{1/2} = \frac{1}{k \cdot a}$,the order of reaction will be: