Question : The distance covered by a particle varies with time and is given by x=at²-bt³. The time 't' of the particle when its acceleration is zero is :
a) a/b
b) b/c
c) a/3b
d) 2a/3b
Doubt by Yathartha
DAV 2023
Solution :
x=at²-bt³
Velocity (v)
v=dx/dt
=d(at²-3bt³)dt
= 2at-3bt²
Now,
Acceleration (A)
A=dv/dt
= d(2at-3bt²)/dt
=2a-6bt
A = 0
2a-6bt=0
2a=6bt
2a/6b=t
t = a/3b
Hence, c) a/3b would be the correct option.