Q.6)
The displacement s of a particle depends on
time t according to the following relation
s =1/3t^3 - t^2 + t. The velocity and displacement
of the particle at the instant when
acceleration is zero, are respectively-
(A)0,1/3
(B) 1/3,0
(C)1/3,1/3
(D) None of the above
Answers
Explanation:
s =1/3t^3 - t^2 + t
v = (1/3 )3t^2 - 2t
a = 2t - 2
When acceleration = 0 , t = 1 s
s = 1/3 - 1 +1 = 1/3 unit
velocity = 1-2 = -1 unit
Given:
displacement equation is given as 1/3 t³ - t² +t
To Find:
The velocity and displacement of the particle at the instant when
acceleration is zero, are respectively.
solution:
displacement s = 1/3 t³ - t² +t
we know that velocity of a particle at any instant is given by,
v= ds/st
= d/dt( 1/3 t³ - t² +t )
v =3t²/3 -2t +1
v = t² - 2t +1
we know that the accelaration of a particle at any point is given by,
a= dv/dt
=d/dt( t² - 2t +1 )
= 2t - 2
according to the question we will find the time when accelaration is 0.
a = 0
2t - 2 = 0
t - 1 = 0
t = 1 sec
put the value of t=1 in velocity and displacement
s = 1/3 t³ - t² +t
=1/3x1 - 1 +1
=1/3
v = t² - 2t +1
= 1 -2 +1
=0
Hence The velocity and displacement of the particle at the instant when acceleration is zero, are respectively are 0 and 1/3 .