Posted by Kenneth on Saturday, November 22, 2008 at 4:57pm.
Two runners, A and B run on a straight race track for 0</=t</=10 seconds. The graph below, which consists of two line segments, shows the velocity, in meters per second, of runner A. The velocity of runner B, in meters per second, is given by the function v defined by v(t)=24t/2t+3/
Although I can't post the graph, there are two points labeled, (3,10) and (10,10).
ind the velocity of runner A and runner B at t=2 seconds. I know you can't see the graph, but is there any way you could guide me on how to do this problem?? thank you

calculus  Kenneth, Saturday, November 22, 2008 at 4:58pm
sorry the slash after the three should actually be a period, the equation is only 24t/2t+3

calculus  Damon, Saturday, November 22, 2008 at 5:02pm
v(t)=24t/(2t+3) [[ Maybe ?????? ]]
Although I can't post the graph, there are two points labeled, (3,10) and (10,10).
[[ and (0,0) ]] maybe????

calculus  Damon, Saturday, November 22, 2008 at 5:08pm
MAKING THOSE ASSUMPTIONS ABOUT WHAT YOU WERE GIVEN!!!!
At two seconds for runner A
I think runner A went from (0,0) to (3,10) in a straight line
then:
y = m x + b
(0,0) > b = 0
m = 10/3
so
y = (10/3)x
for x = 2 y = 20/3 or 6.67
Runner B if y = 24 x / (2x+3)
where x = 2
y = 48 / (4+3) = 48/7 = 6.86

calculus  Kenneth, Saturday, November 22, 2008 at 5:40pm
thank you so much! as a follow up question, for acceleration of the two runners, is acceleration the anti derivative of velocity???

calculus  Damon, Saturday, November 22, 2008 at 5:48pm
No!!!
acceleration = dv/dt

calculus  Damon, Saturday, November 22, 2008 at 5:55pm
dv/dt for A = 10/3 (constant slope until t = 3)
dv/dt for B
v(t)=24t/(2t+3)
a = dv/dt = [(2t+3)(24) 24t(2) ]/(2t+3)^2
put in t = 2
a(2) = dv/dt = [ 7(24) 96 ] /(49)
= 72/49 = 1.47

calculus  Damon, Saturday, November 22, 2008 at 5:56pm
By the way, position is the antiderivative of velocity
Answer This Question
Related Questions
 Physics  Near the end of a marathon race, the first two runners are separated ...
 Physics  Two runners have a race. The first runner decides to run with his full...
 Physics  During a rElay race along a straight ROAD the 1st runner on a three ...
 physics..............  If you ever watch track and field at the Olympics, you'...
 physics!!!!!!!!!!  If you ever watch track and field at the Olympics, you'll ...
 algebra  Two persons are to run a race, but one can run 8 meters per second, ...
 algebra  Two persons are to run a race, but one can run 10 meters per second, ...
 Physics  A relay race is run along a straight line track 300.0 m long running ...
 Physics  A runner completes an 850m race with two laps of the 425m track in the...
 Maths  Three runners run a 10 metre race. Each runner runs according to the ...
More Related Questions