Q.
A particle moving with uniform acceleration has average velocities v1,v2 and v3 over the successive intervals of time t1,t2 and t3 respectively. The value of (v2−v3)(v1−v2) will be
Let u be initial velocity and a be uniform acceleration.
Average velocities in the intervals from
0 to t1,t1 to t2 and t2 to t3 are v1=2u+u+at1=u+2at1…(i) v2=2u+at1+u+a(t1+t2)=u+at1+2at2…(ii) v3=2u+a(t1+t2)+u+a(t1+t2+t3) =u+at1+at2+2at3…(iii)
Subtract (i) from (ii), we get; v2−v1=2a(t1+t2)…(iv)
Subtract (ii) from (iii), we get; v3−v2=2a(t2+t3)…(v)
Divide (iv) by (v), we get v3−v2v2−v1=(t2+t3)(t1+t2)
or v2−v3v1−v2=(t2+t3)(t1+t2)