# calculus

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

1. 👍 0
2. 👎 0
3. 👁 821
1. sorry the slash after the three should actually be a period, the equation is only 24t/2t+3

1. 👍 0
2. 👎 0
2. 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????

1. 👍 0
2. 👎 0
3. 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

1. 👍 0
2. 👎 0
4. thank you so much! as a follow up question, for acceleration of the two runners, is acceleration the anti derivative of velocity???

1. 👍 0
2. 👎 0
5. No!!!
acceleration = dv/dt

1. 👍 0
2. 👎 0
6. thank you so much or your help! as a follow up question, for acceleration of the two runners, is acceleration the anti derivative of velocity???

1. 👍 0
2. 👎 0
7. 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

1. 👍 0
2. 👎 0
8. By the way, position is the anti-derivative of velocity

1. 👍 0
2. 👎 0

## Similar Questions

1. ### mathematics

A circular race track is being built. The outsidediameter of the track is 200 feet, and the inside diameter is 180 feet. If two runners run around the track once, with one of them running on the outside edge of the track, while

2. ### physics

A race car traveling northward on a straight, level track at a constant speed travels 0.750km in 20.0s. The return trip over the same track is made in 25.0s. What is the average velocity of the car in m/s for the first leg of the

3. ### math

three pigs entered a race around a track. Piggly takes 6 minutes to run one lap, piglet takes 3 minutes while wiggly takes 5 minutes. If all three pigs begin the race at 1:00pm at what time will all be at the starting point again?

4. ### English

Which sentence describes a race car using onomatopoeia? A. The sweet car went around the track quickly. B. The rapid race car drove around the track. C. The fast car traveled around the roadway D. The sleek, powerful race car

1. ### Math

Three pigs entered a race around a track. Piggly takes 6 minutes to run one lap. Piglet takes 3 minutes to run one lap and it takes Wiggly 5 minutes to run one lap. If all three pigs begin the race at the same time, how many

2. ### College Algrebra

Joel can run around a 1/4 mi track in 66 sec. Jason can run around the track in 60 sec.If the runners start at the same point on the track and run in opposite directions, how long will it take the runners to cover 1/4 mile?

3. ### Math

one track coach wants his athletes to race 8 miles around a track to measure how fast each person can run if the track is 2/3 of a mile around. How many laps around the track will the athletes have to run to complete the race?

4. ### math

Jon begins jogging at a steady 3m/sec down the middle of lane one of a public track. Laura starts even with him in the center of lane two but moves 4m/sec. At the instant they begin, Ellie is located 100 meters down he track in

1. ### ELA and Please Hurry!!!!

Not only is the race special because it takes place on a special day, but it also has a rich, over three-decade tradition. While the Boston Marathon can declare it is the oldest road race in America, few 10K’s can claim

2. ### Physics

During 200 meter and 400 meter races, runners must stay in lanes as they go around a curved part of the track. If runners in two different lanes have exactly the same speed, will they also have exactly the same centripetal

3. ### Physics

A circular track has several concentric rings where people can run at their leisure. Phil runs on the outermost track with radius rP while Annie runs on an inner track with radius rA = 0.90 rP. The runners start side by side,

4. ### Maths

In a race, each of the four greyhounds run at its own constant speed. They all start at the same point on a circular track and at 30 seconds into the race, while all are still on their first lap, they have spread out so they are