Question

2. The distance travelled by a particle is directly proportional to the square of the time aken (soth
The acceleration of the particle is :
(a) increasing
(b) decreasing (c) zero
(d) constant
graph gives :​

Answer 1

Answer:

Constant

Explanation:

If no extra force acts on it then it remains constant

Answer 2

The acceleration of the particle is (d) constant.

Given:

The distance traveled by a particle is directly proportional to the square of the time taken.

To Find:

acceleration of particle

Solution:

As given information,

⇒ x ∝ t²         where x is distance traveled,

⇒  x = kt²       k is constant and t is time taken

as we know,

velocity =  $\frac{dx}{dt}$

⇒ x = kt²

differeniate w.r.t. x

⇒  $\frac{dx}{dt}$ = 2kt

acceleration = $\frac{d^{2}x }{dt^{2} }$

⇒  $\frac{d^{2}x }{dt^{2} }$ = 2k

acceleration = constant

Hence, the acceleration of the particle is constant.