Question 161: Motion in 1D

Question

The displacement x of a particle varies with time t as x = ae
$$-$$at
+ be
$$\beta $$t
, where a, b, $$\alpha $$ and $$\beta $$ are positive constants. The velocity  of the particle will

Accepted Answer

x = ae
$$-$$$$\alpha $$t
+ be
$$\beta $$t
$${{dx} \over {dt}}$$ = - $$\alpha $$ae
$$-$$$$\alpha $$t
+ b$$\beta $$e
$$\beta $$t
v =  - $$\alpha $$ae
$$-$$$$\alpha $$t
+ b$$\beta $$e
$$\beta $$t
Velocity will go on increasing with time.

Answer

be independent of $$\beta $$

Answer

drop to zero when $$\alpha $$ = $$\beta $$

Answer

go on decreasing with time

Answer

go on increasing with time.

Motion in 1D

The displacement x of a particle varies with time t as x = ae $-at + be \beta t , where a, b, \alpha and \beta $ are positive constants. The velocity of the particle will

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