Question

prove that V2=U2+2as​

Answer 1

Explanation:

We know that,

dv⃗dt=a⃗

Multiplying and dividing LHS by ds⃗

⟹dv⃗ds⃗ds⃗dt=a⃗

We replace ds⃗dt with v⃗ to get

v⃗dv⃗ds⃗=a⃗

⟹v⃗dv=a⃗ds

We know that at S=0,V=u and at S=s,V=v ,

Integrating both sides with appropriate limits:

⟹∫vuvdv=∫s0ads

⟹v22|vu=as|s0

⟹v22−u22=a(s−0)

⟹v2−u22=as

⟹v2−u2=2as

⟹v2=u2+2as

Or more appropriately,

v⃗⋅v⃗=u⃗⋅u⃗+2a⃗⋅s⃗

Answer 2

Please find the attached photograph for your answer