After 35 minutes of jogging, at the 9-km point in a total 10-km race, jogger A 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
Also for the last question regarding the donuts I used your method for part b and it said the answer is wrong. It want s the answer in meters.
Need to know how far behind runner A is at 9 km
then figure time for leader to run the last km at 9 km /35 min rate
In that time A mus increase speed so that he covers 1 km plus the distance behind in that time
his average speed is then (1 + distance behind)/time for leader to finish
his final speed is then found from
average speed = (final + original)/2
then the constant acceleration is
a = (final speed - original speed)/time
To determine the acceleration required for jogger A to catch up to the finish line, we can use the equation of motion:
s = ut + (1/2)at^2
where:
s = total displacement
u = initial velocity
t = time
a = acceleration
In this scenario, the leader has already covered 9 km in 35 minutes, so their initial displacement is 9 km. Jogger A would need to cover the remaining 1 km to catch up to the finish line.
From the given information, we know the time taken by jogger A is also 35 minutes (since they are moving at the same speed as the leader), which is equivalent to 35/60 = 0.5833 hours. Therefore, t = 0.5833 hours.
Since we want to find the acceleration, we need to rearrange the equation to solve for a:
a = (2s - 2ut) / t^2
Substituting the known values into the equation:
a = (2 * 1 km - 2 * 0 km) / (0.5833 hours)^2
a = (2 * 1 km) / (0.5833 hours)^2
Calculating the numerator:
2 * 1 km = 2 km
Calculating the denominator:
(0.5833 hours)^2 = 0.3403 hours^2
Now, divide the numerator by the denominator to find the acceleration:
a = 2 km / 0.3403 hours^2
a ≈ 5.87 km/h^2
Therefore, the correct answer for the required acceleration is approximately 5.87 km/h^2, not 3.7.
Regarding your previous question about the donuts, if you used the method provided for part b and received an incorrect answer in meters, please provide the details of your calculations so that I can help you identify the mistake.