Question

equation √ X equal to t + 9 gives the variation of displacement with time show that acceleration of particle is constant

Answer 1

it is given that , √x = t + 9

squaring both sides, we get

x = (t + 9)² = t² + 18t + 81

we know, acceleration is the rate of change of velocity with respect to time and velocity is the rate of change of displacement with respect to time.

so, acceleration , a = d²x/dt²

means, to find acceleration, we have to differentiate x twice with respect to time.

first differentiation, dx/dt = d(t² + 18t+81)/dt = 2t + 18

2nd differentiation, d²x/dt² = d(2t+18)/dt = 2

hence, d²x/dt² = a = 2

here it is clear that acceleration is a constant term. so, particle moves with uniform (or constant) acceleration.

Answer 2

Answer:

Explanation:

Equation √x = t + 9 (Given)

Acceleration is defined as the rate of change of velocity of an object with the respect to time. The acceleration of an object is the net result of all the forces acting on the object,

Thus, acceleration =  F = ma or

a = d²x/dt² ( which means that equals change in velocity (Δv) is divided by change in time (Δt).

Squaring both sides of the given equation we will get -  

x = (t + 9)²

= t² + 18t + 81

First differentiation -

dx/dt = d(t² + 18t+81)/dt

= 2t + 18

Second differentiation -

d²x/dt² = d(2t+18)/dt

= 2

Thus, d²x/dt² = a = 2

Since, acceleration is a constant, thus the particle will move with a uniform acceleration.