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A particle is at x=+5m at t=0, x=-7m at ...

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`.

Text Solution

Verified by Experts

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)`
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