The displacement 'X' of a particle moving along a straight line at time t is given by x=a0+a1t+a2t2 The acceleration of the particle is:

Question

The displacement 'X' of a particle moving along a straight line at time t is given by x=a0+a1t+a2t2 The acceleration of the particle is: (A)  4a2  (B)  2a2  (C)  2a1  (D)  a2

Tardigrade Admin · Accepted Answer

Acceleration is known as rate of change of velocity.
The given equation is

x = a_{0} + a_{1} t + a_{2} t^{2}

First differentiate the above equation with respect to t, to obtain velocity that is,

v = \frac{d x}{d t}

(velocity is rate of change of displacement)

∴

v = \frac{d x}{d t} = a_{1} + 2 a_{2} t

(using \frac{d}{d x} x^{n} = n x^{n - 1})

Then second differentiation of above equation gives acceleration i.e.,

a = \frac{d y}{d t} = 2 a_{2}

Q. The displacement 'X' of a particle moving along a straight line at time t is given by
$x = a_{0} + a_{1} t + a_{2} t^{2}$
The acceleration of the particle is:

$4 a_{2}$

$2 a_{2}$

$2 a_{1}$

$a_{2}$

Q. The displacement 'X' of a particle moving along a straight line at time t is given by x=a0​+a1​t+a2​t2 The acceleration of the particle is:

4a2​

2a2​

2a1​

a2​

Q. The displacement 'X' of a particle moving along a straight line at time t is given by
$x = a_{0} + a_{1} t + a_{2} t^{2}$
The acceleration of the particle is:

$4 a_{2}$

$2 a_{2}$

$2 a_{1}$

$a_{2}$