A particle is at x=+5m at t=0, x=-7m at t=6s and x=+2m at t=10s. Find the average velocity of the particle during the intervals (a) t=0 to t=6s (b) t=6s to t=10s (c ) t=0 to t=10s.

A particle is at x=+5m at t=0, x=-7m at t=6s and x=+2m at t=10s. Find

1.	A particle is at x=+5m at t=0, x=-7m at t=6s and x=+2m at t=10s. Find the average velocity of the particle during the intervals (a) t=0 to t=6s (b) t=6s to t=10s (c ) t=0 to t=10s.
Answer» Solution :From the DEFINITION of AVERAGE VELOCITY `V=(Deltax)/(Deltat)=(x_(2)-x_(1))/(t_(2)-t_(1))` (a) The average velocity between the times `t=0` to `t=6s` `x_(1)=+5m,t_(1)=0,x_(2)=-7mt_(2)=6s` Hence `v_(1)=(x_(2)-x_(1))/(t_(2)-t_(1))=(-7-5)/(6-0)=-2ms^(-1)` (b) The average velocity between the times `t_(2)=6s` to `t_(3)=10S` is `v_(2)=(x_(3)-x_(2))/(t_(3)-t_(2))=(2-(-7))/(10-6)=(9)/(4)=2.25ms^(-1)` (c ) The average velocity between times `t_(1)=0` to `t_(3)=10s` is `v_(3)=(x_(3)-x_(1))/(t_(3)-t_(1))=(2-5)/(10-0)=-0.3ms^(-1)`