The displacement x of a particle varies with time t as x=ae raised to power minus alpha into t+ be raised to power beta into t. a, b, alpha, beta are positive constants. Then velocity of particle? Ans is increases with time... can u explain why??

I don't understand the equation, especially your phrase "minus alpha into t+ be raised to power beta into t." Please write it out using '^' to signify a power and with proper use of parentheses. Do you mean this: x = ae^(-alpha t + beta t)? If so, whether it is continuously increasing or not depends on the values of alpha and beta. Are the values of a, alpha, and beta all positive values?

**EDIT** OK, I think you may have meant this:

x(t) = ae^{-\alpha t} + b e ^{\beta t}

Hint: from the displacement equation you can derive the equations for velocity and acceleration. If velocity is always increasing with time, what property must the acceleration function have for all values of t?