$A$ catalyst

The activation energy of a chemical reaction can be determined by:

Why does the rate of a reaction increase with a rise in temperature?

The rate constant is doubled when temperature increases from $27^{\circ} C$ to $37^{\circ} C$. What is the activation energy in $kJ \ mol^{-1}$?

The rate constant of a reaction varies with temperature according to the equation: $\log K = \text{constant} - \frac{E_a}{2.303 RT}$. If a plot of $\log K$ versus $1/T$ yields a straight line with a slope of $-5632$,then the activation energy of the reaction is .......... $kJ \ mol^{-1}$.

The rate of reaction is tripled for a $10^\circ C$ rise in temperature. The increase in the reaction rate if the temperature is increased by $60^\circ C$ is $............$ times.