Question

831 The position x (t) of a particle at any time (t) is given by
x (t) = 4t^3
- 3 t2 + 2
The acceleration and velocity of the particle will be zero at
time t = 2 s are respectively
(A) 12 m s-2 and 25 m s-1 (B) 16 m s-2 and 22 m s-1
(C) 42 m s-2 and 36 m s-1 (D) 48 m s-2 and 36 m s-1
(A.I.I.M.S. 2009)​

Answer 1

Answer:

ANSWER

Position of the particle x=2t

2

−t

3

Velocity v=

dt

dx

=4t−3t

2

Acceleration a=

dt

dv

=4−6t

So, a( at t=2 s)=4−6×2=−8 m/s

2

Since, acceleration is depending on the time. SO, acceleration is not constant.

Answer 2

Position of the particle x=2t

2

−t

3

Velocity v=

dt

dx

=4t−3t

2

Acceleration a=

dt

=4−6t

So, a( at t=2 s)=4−6×2=−8 m/s

2

Since, acceleration is depending on the time. SO, acceleration is not constant.