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

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

1.	A particle is at x=+5 m at t=0, x=-7m at t=6 s and x =+2 at t=10s.Find the averahe velocity of the particle during the intervals (a)t=0 to t=6s (b)t=6s to t=10s, ©t=0 to t=10 s.
Answer» Solution :From the defination of AVERAGE velocity `V=(trianglex)/(trianglet)=(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)=-7m t_(2)=6s` HENCE `v_(1)=(x_(2)-x_(1))/(t_(2)-t_(1))=(-7-5)/(6-0)=-2ms^(-1)` (b) The average veloctiy 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)=10` s is `v_(3)=(x_(3)-x_(1))/(t_(3)-t_(1))=(2-5)/(10-0)=-0.3ms^(-1)`