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 anti-derivative of velocity

## Answer this Question

## Related Questions

- 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 ...
- Physics - Two runners have a race. The first runner decides to run with his full...
- 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 running track consists of two straight 88.5m segments and two ...
- Physics - During a rElay race along a straight ROAD the 1st runner on a three ...
- Physics - A runner completes an 850m race with two laps of the 425m track in the...
- math - Two runners are competing in a race. One runner averages a pace of 7 ...

More Related Questions