Speed Up to Catch Leader in 10km Race

In summary: That way you can have a constant acceleration and work out the correct v at the end.In summary, to catch up to the leader at the finish line after being 100m behind at the 9km point in a 10km race, the slower runner would need to accelerate at a rate of 0.43 m/s^2. This would allow them to reach the finish line at the same time as the leader, assuming the leader maintains a constant speed.
  • #1
negation
818
0
After 35mins of runnin, at the 9km point in a 10km race, you find yourself 100m behind the leader and moving at the same speed.
What should your acceleration be if you're to catch up by the finish line? Assume that the leader maintains constant speed.
 
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  • #2
Please show your own attempt.
 
  • #3
vf = 9000m/35min = 257m min^-1
vf = 9100m/35min = 260 min^-1

10,000-9100m = 900m
900m/ 260m min^-1 = 3.46min

Runner requires 3.46min to tie the leader at the finish line.

xf - xi = 0.5(vf + vi)t
1000m = 0.5(vf+257m min^-1)3.46min
vf = 321m min^-1

vf doesn't tally with the answer sheet
 
  • #4
Can someone help me? I've spent 4 hrs on this question already. I don't want to get into the unhealthy habit of not sleeping for days until I figure out the answer.
 
  • #5
The numbers that are significant in this problem are the 1000 m that the slower runner needs to cover, and the 900 m that the faster runner has left.

Don't use the same variable for both runners:
negation said:
vf = 9000m/35min = 257m min^-1
vf = 9100m/35min = 260 min^-1
vf can't possibly be equal to two different numbers.
 
  • #6
vf = 9000m/35min = 257m min^-1
vf = 9100m/35min = 260 min^-1

10,000-9100m = 900m
900m/ 260m min^-1 = 3.46min

I agree. You have to get to the finish in less than 3.46min.

Than I would look at one of the SUVAT equations to work out the minimum constant acceleration required. http://en.wikipedia.org/wiki/Equations_of_motion

Perhaps this one and solve for a...

s = ut + 0.5at2

You know..

s = 900m
u = 257m/min or 4.28m/S
t = 3.46min or 207.6 seconds
 

Related to Speed Up to Catch Leader in 10km Race

1. How can I increase my speed in a 10km race to catch the leader?

To increase your speed in a 10km race, you can incorporate speed training into your regular running routine. This can include interval training, hill repeats, and tempo runs. Additionally, make sure you are eating a balanced diet and getting enough rest to support your body's ability to run faster.

2. Is it possible to catch the leader in a 10km race if they have a significant lead?

It is definitely possible to catch the leader in a 10km race, even if they have a significant lead. However, it will require a lot of effort and strategic planning. You will need to pace yourself, maintain a consistent speed, and use the terrain to your advantage.

3. How important is proper form in increasing speed during a 10km race?

Proper form is crucial in increasing your speed during a 10km race. A good running form can help improve your efficiency and reduce the risk of injuries. Make sure to maintain a tall posture, keep your arms and shoulders relaxed, and take short and quick strides.

4. Should I focus on increasing my speed or my endurance in a 10km race?

It is important to have a balance of both speed and endurance in a 10km race. Endurance will help you maintain your pace throughout the race, while speed will help you catch up to the leader. Incorporate both speed and endurance training into your regular routine to prepare for the race.

5. Can mental strategies help me catch the leader in a 10km race?

Yes, mental strategies can be very helpful in catching the leader in a 10km race. Visualizing yourself catching up to the leader, breaking the race into smaller segments, and focusing on your breathing can all help you stay motivated and determined throughout the race.

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