Question

derive the distance travelled in the n of uniformly accelerate motion​

Answer 1

Question:-

Derive the distance travelled in the n of uniformly accelerate mmotion or derive $\sf \:s_n=u+a(n1/2)$

Answer:

• Let a particle moving with uniform acceleration ‘a’.
• Let u be the initial velocity of the particle

$\therefore$Distance travelled during nth second = Distance travelled in ‘n’ seconds – Distance travelled in (n-1) seconds

Step-by-step explanation:

$\sf \:s_n=un+1/2an^2 –[u(n−1)+1/2a(n−1)^2 ]$

$\sf \:=un+1/2an^2–[un−u+1/2a(n^2 −2n+1)]$

$\sf \:=un+1/2an^2 –[un−u+1/2an^2−an+1/2a]$

$\sf \:=un+1/2an^2–un+u–1/2an^2+an–1/2a$

$\sf \:=u+an–1/2a$

$\sf \:s_n=u+a(n–1/2)$