Q. The displacement x of a particle varies with time t as x = ae^(−αt) + be^(βt), where a, b, α and β are positive constants. The velocity of the particle will :
A) go on decreasing with time
B) be independent of α and β
C) drop to zero when α = β
D) go on increasing with time
Explanation
[Solution from source] v = −aαe^(−αt) + bβe^(βt) and dv/dt = aα²e^(−αt) + bβ²e^(βt) > 0 for all t, so the velocity keeps increasing. It clearly depends on α and β, and α = β does not make it zero for all times. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.