Categories > Motion in A Straight Line > non-uniform-motion > The displacement \[x\] of a particle varies with time \[t,x = a{e^{ - \alpha t}} + b{e^{\beta t}}\], where \[a,\,b,\,\alpha \,{\rm{and }}\beta \]are positive constants. The velocity of the particle will [CBSE PMT 2005]

Motion in A Straight Line

Question: The displacement \[x\] of a particle varies with time \[t,x = a{e^{ - \alpha t}} + b{e^{\beta t}}\], where \[a,\,b,\,\alpha \,{\rm{and }}\beta \]are positive constants. The velocity of the particle will [CBSE PMT 2005]


1) Go on decreasing with time
2) Be independent of \[\alpha \] and \[\beta \]
3) Drop to zero when \[\alpha = \beta \]
4) Go on increasing with time
Solution: Explanation: Explanation
non-uniform-motion

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