Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Introductory Physics Homework Help
Relationship Between Velocities of Two Runners
Reply to thread
Message
[QUOTE="Drakkith, post: 5126268, member: 272035"] [h2]Homework Statement [/h2] Reginald is out for a morning jog, and during the course of his run on a straight track, he has a velocity that depends upon time as shown in the figure below. That is, he begins at rest, and ends at rest, peaking at a maximum velocity [I]V[/I][SUB]max[/SUB] at an arbitrary time [I]t[/I][SUB]max[/SUB]. A second runner, Josie, runs throughout the time interval [I]t[/I] = 0 to [I]t[/I] = [I]t[/I] [SUB]f[/SUB] at a constant speed [I]V[SUB]j[/SUB][/I], so that each has the same displacement during the time interval. Note: [I]t[/I] [SUB]f[/SUB] is NOT twice [I]t[/I] [SUB]max[/SUB] , but represents an arbitrary time. What is relation between [I]V[SUB]j[/SUB][/I] and [I]t[/I][SUB]max[/SUB]? [h2]Homework Equations[/h2] Position equation for constant acceleration: X=X[SUB]i[/SUB]+V[SUB]i[/SUB]+1/2AT[SUP]2[/SUP] Velocity Equation for constant acceleration: V=V[SUB]i[/SUB]+AT Position Equation for constant velocity: X=X[SUB]i[/SUB]+VT [ATTACH=full]178855[/ATTACH] [B] 3. The Attempt at a Solution [/B] Not sure what to do really, so I've just been trying things. The only commonality between the two runners is the final position X and the time t[SUB]f[/SUB] For Josie, X = V[SUB]j[/SUB]t[SUB]f[/SUB] For Reginald: Velocity: From t[SUB]i[/SUB] to t[SUB]max[/SUB], V[SUB]max[/SUB] = At[SUB]max[/SUB] From t[SUB]max[/SUB] to t[SUB]f[/SUB], since V[SUB]f[/SUB] = 0, the equation is: 0 = V[SUB]max[/SUB] + At[SUB]f[/SUB] Position: From t[SUB]i[/SUB] to t[SUB]max[/SUB], initial displacement and velocity are zero: X[SUB]1[/SUB] = 1/2At[SUB]max[/SUB][SUP]2[/SUP] From t[SUB]max[/SUB] to t[SUB]f[/SUB]: X = X[SUB]1[/SUB] + V[SUB]max[/SUB]t[SUB]f[/SUB] + 1/2At[SUB]f[/SUB][SUP]2[/SUP]Since X = V[SUB]j[/SUB]t[SUB]f[/SUB], we can rewrite the above equation as: V[SUB]j[/SUB]t[SUB]f[/SUB] = X[SUB]1[/SUB] + V[SUB]max[/SUB]t[SUB]f[/SUB] + At[SUB]f[/SUB][SUP]2[/SUP] Replacing X[SUB]1[/SUB] with its equation: V[SUB]j[/SUB]t[SUB]f[/SUB] = 1/2At[SUB]max[/SUB][SUP]2[/SUP]+ V[SUB]max[/SUB]t[SUB]f[/SUB] + At[SUB]f[/SUB][SUP]2[/SUP] That's about as far as I've gotten and I don't know if I'm even on the right track. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Introductory Physics Homework Help
Relationship Between Velocities of Two Runners
Back
Top