wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The displacement x of a particle varies with time according to the relation, x=ab(1−e−bt). Then the correct statements is/are

A
at t = 1/b, the displacement of the particle in nearly 2a3b.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
the velocity and acceleration of the particle at t=0 are a and ab respectively.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
the particle cannot reach a point at a distance x from its starting position if x>ab.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
all of the above
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is B all of the above
x=ab(1ebt)
At t= 1/b , x=ab(11e)
Therefore, option A is correct.
11e is approximately 2/3. Hence x=23a/b
Maximum value of x is a/b, given t is positive.
Therefore, option C is correct.
Differentiating with t,
Velocity u=dxdt=ab(+bebt)=aebt
u=a at t=0
Differentiating velocity with t,
Acceleration=d2xdt2=aebt(b)=abebt
acceleration =ab at t=0
Therefore, option B is correct.
Hence, correct option is D

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Aftermath of SHM
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon