2. A position–time graph for a particle moving along the x axis is shown in Figure P2.5. (a) Find the average velocity in the time interval `t = 1.50 s` to `t = 4.00 s`. (b) Determine the instantaneous velocity at `t = 2.00 s` by measuring the slope of the tangent line shown in the graph. (c) At what value of `t` is the velocity zero?
`overline(v) = (∆x)/(∆t)`
(a) `-2.4m//s` (b) `-3.7m//s` (c) `4s`
(a) From given graph red curve: `x(1.50) = 8.0\ m` `x(4.00) = 2.0\ m` `overline(v) = (2.0m - 8.0m)/(4.00s - 1.5s) = color(red)(-2.4m//s)` (b) From given graph green line we get : `x(0) = 13.0m` `x(3.5) = 0 m` slop of green line, which is the instantaneous velocity: `v = (0m-13.0m)/(3.5s-0s) = color(red)(-3.7 m//s)` (c) The velocity equals 0 when the slope of the tangent equals 0. And the slope of the tangent equals 0 when it's parallel to the time axis in given graph, where `t = 4s`.