The displacement x of a particle varies with time t as x = ae- t + be t, where a, b, and are positive constants. The velocity of the particle will
- be independent of
- drop to zero when =
- go on decreasing with time
- go on increasing with time.
Answer
(4) go on increasing with time.
Solution
v = dxdt = -a e- t + b e t
dvdt = a 2 e- t + b 2 e t
a, b, , are positive, both terms are positive dvdt > 0 at all times
The velocity goes on increasing with time.
Answer: (4)