After 35 minutes of jogging, at the 9-km point in a total 10-km race, jogger 1 is behind the leader and moving at the same speed. What would have to be your accelearation in order to catch up to the finish line? Assuming the leader maintains a constant speed the rest of the race.
Is the answer 3.7
1 what behind the leader? 1 km? I will assume so. After 35 minutes, runner 1 would then have 1 km to go and runner 2 would have 2 km to go. The race will be over in 1 km/(9 km/35 min) = 35/9 = 3.89 minutes. Runner 2 must have an average speed over the last 2 km of
2km/3.59 min = 0.557 km/min to catch up. He started the "finishing kick" at a speed of 8 km/35 min = 0.229 km/min and will have to end it at 0.656 km/min. Such a speed is not humanly possible.
I will leave you to compute the required acceleration. (A 0.427 km/min increase in speed in 3.89 minutes)
To find the required acceleration to catch up to the finish line, we need to determine the time it would take for Jogger 1 to reach the finish line and compare it to the time it would take for the leader to reach the finish line.
Since Jogger 1 is 9 km into the race after 35 minutes, we can calculate their current speed:
Speed = Distance / Time
Speed = 9 km / (35 minutes / 60 minutes per hour) ≈ 15.43 km/h
Now, assuming the leader maintains a constant speed, Jogger 1 would need to cover the last kilometer in the time difference between the leader's finishing time and Jogger 1's current time.
The time difference between Jogger 1 and the leader would be 35 minutes since Jogger 1 started 35 minutes earlier. Therefore, the leader will finish in (35 minutes + 35 minutes) = 70 minutes.
Now, to calculate the acceleration needed, let's determine how much time it would take Jogger 1 to cover the remaining 1 km at their current speed:
Time = Distance / Speed
Time = 1 km / (15.43 km/h) ≈ 0.065 hours ≈ 3.9 minutes
To catch up to the leader at the finish line, Jogger 1 needs to complete the remaining 1 km in 3.9 minutes (considering the leader's finishing time of 70 minutes).
To find the required acceleration, we need to calculate the change in velocity (Δv) over time (Δt):
Acceleration = Δv / Δt
Acceleration = (Final Velocity - Initial Velocity) / Time
Since Jogger 1 is moving at the same speed as the leader, their initial and final velocities are the same. Therefore, the change in velocity will be 0.
Acceleration = 0 / 3.9 minutes ≈ 0 m/s²
Hence, the required acceleration for Jogger 1 to catch up to the finish line is approximately 0 m/s², as no additional acceleration is needed once they are already moving at the same speed as the leader.