Two people, Paige and Sandy, are racing each other. Assume that both their accelerations are constant, Paige covers the last 1/8 of the race in 5 seconds, and Sandy covers the last 1/5 of the race in 8 seconds. Who wins, and by how much?
let Page's acceleration be a
let Sandy's acceleration be b
Page's velocity is at + c
Sandy's velocity is bt + k
at t=0, both their velocities should have been zero, so c = 0, k=0
then if the distance of the race is x units
then for Page: 5a = x/8 ---> x = 40a
for Sandy : 8b = x/5 ---> x = 40b
40a = 40b
a = b
they have the same velocity.
It is a tie ?
Am I missing something here?
You forgot to include velocity. Using the equation distance= 1/2at^2+vt, one can plug in t (time) and distance.
To determine who wins the race and by how much, we need to compare the distances covered by Paige and Sandy. Let's use the variables "d_P" for Paige's distance and "d_S" for Sandy's distance.
First, let's find the total distance of the race by finding a common denominator for 1/8 and 1/5. The least common multiple of 8 and 5 is 40. Therefore, the total race distance is 40 units.
Next, we can calculate the distances covered by Paige and Sandy. Since both their accelerations are constant, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
For Paige, she covers the last 1/8 of the race distance in 5 seconds. Therefore, her distance can be calculated as:
d_P = (1/8) * 40 = 5 units
For Sandy, she covers the last 1/5 of the race distance in 8 seconds. Therefore, her distance can be calculated as:
d_S = (1/5) * 40 = 8 units
Now that we have the distances covered by both racers, we can determine who wins and by how much.
Since Paige's distance covered is less than Sandy's, Sandy wins the race. The difference in their distances is:
d_S - d_P = 8 - 5 = 3 units
Therefore, Sandy wins the race by 3 units.