Question

If a particle ‘s motion is described as x= ut + 1/2 a1t^2 , where x is position , t is the time and u and a1 , are constants . Show that acceleration of the particle is constant . no copying from, meritnation or google

Answer 1

Given:

Equation of the path travelled by particle,

x= ut+ ½a₁t²

where u and a₁ are constants

To Prove:

Acceleration of given particle is constant

Solution:

We know that,

• Velocity of a body 'v' is given by

v = dx/dt

• Acceleration of a body 'a' is given by

a = dv/dt

where,

x is the displacement of particle at time t

━━━━━━━━━━━━━━━━━━━━━

Let the velocity of given particle be v and acceleration of given particle be a

So,

v= dx/dt

v= d(ut+ ½a₁t²)/dt

v= u(1)+ ½a₁×2×t

v= u+a₁t

Also,

a= dv/dt

a= d(u+a₁t)/dt

a= 0+a₁(1)

a= a₁

And it is given that a₁ is constant

So, acceleration of given particle is constant.