Home
Class 11
PHYSICS
For a particle moving with constant acce...

For a particle moving with constant acceleration, prove that the displacement in the `n^(th)` second is given by
`s_(n^(th)) = u + (a)/(2)(2n-1)`

Text Solution

Verified by Experts

From `s= ut + (1)/(2) at^(2)`
`" "s_n =un + (1)/(2) an^(2) ………. (1)`
`" "s_(n-1) = u(n-1) + (1)/(2) a (n-1)^(2)………. (2)`
By equation (1) & (2)
`s_n- s_(n-1)= s_(n^(th))= u + (a)/(2)( 2n-1)`
Promotional Banner

Topper's Solved these Questions

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN|Exercise BEGINNER S BOX-1|6 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN|Exercise BEGINNER S BOX-2|7 Videos

  • KINEMATICS

    ALLEN|Exercise Integer Type Question|3 Videos

  • MISCELLANEOUS

    ALLEN|Exercise SUBJECTIVE QUESTION|9 Videos

Similar Questions

Explore conceptually related problems

A particle with initial velocity u is moving with uniform acceleration (a). The distance moved by the particle in the t^(th) second is given by S=u+(1)/(2)a(2t-1) The dimensions of S must be

A particle starts moving with acceleration 2 m//s^(2) . Distance travelled by it in 5^(th) half second is

Use integeration technique to prove that the distance travelled in nth second: s_nth=u+frac(a)(2)(2n-1)

The distance travelled by a body moving along a straight line with uniform acceleration (a) in the nth second of its motion is given by S_(n)=u+(a)/(2)(2n-1) . This equation is

Find the sum to n term of the series whose n^(th) term is given by n(n^(2) + 1)

Find a_(1),a_(2),a_(3) if the n^(th) term is given by a_(n)=(n-1)(n-2)(3+n)

A particle having initial velocity u moves with a constant acceleration a for a time t. a. Find the displacement of the particle in the last 1 second . b. Evaluate it for u=5m//s, a=2m//s^2 and t=10s .

A particle is initially at rest. It starts moving with a constant acceleration, the speed of the particle in t seconds is 50m/s and after one second the speed becomes 75m/s. calculate the acceleration of the particle and distance covered in (t+1)^("th") second of its motion.

Find the sum to n terms of the series,whose n^(th) terms is given by: (2n-1)^(2)