In order to pass a physical education class at a university, a student must run 1.0 mi in 12.5 min. After running for 10.0 min (assume constant speed), she still has 510 yd to go. What constant acceleration does she need over the final 510 yd in order to make it?
1 mile=1760 yards
First find the constant speed she was running at
speed=distance/time
to find distance subtract 1760-510=1250 yards
1250/10
with this answer divide it by 10 minutes
(125 yd/m)That will be our speed in yards per minute
Next she needs to make 510 yards in 2.5 minutes based on the info given
In order to complete the mile she will need to run 204 yards per minute
to get 204 just divide 510/2.5
acceleration = final velocity - initial velocity/change in time
For this problem treat your speed as velocity
204-125/2.5
This will be your acceleration needed
be sure to put your units (m/s^2)
IMPORTANT: Make sure you convert your final answer to meters and seconds
yeah
To find the constant acceleration needed over the final 510 yards, we need to first calculate the initial velocity of the student and then use the kinematic equation.
Step 1: Calculate the initial velocity (v0) of the student.
Since the student has been running for 10 minutes already, we can calculate the distance covered in 10 minutes:
Distance covered in 10 minutes = (Speed) x (Time) = (1 mile/12.5 minutes) x (10 minutes)
Converting miles to yards, we have:
Distance covered in 10 minutes = (1 mile/12.5 minutes) x (10 minutes) x (1760 yards/1 mile)
Step 2: Calculate the initial velocity (v0) using the formula:
v = v0 + at
In this case, the final velocity (v) is zero since the student needs to stop running after completing the final 510 yards. Hence, the equation becomes:
0 = v0 + at
Step 3: Calculate the acceleration (a) using the relation between distance (d) and acceleration:
d = v0t + (1/2)at^2
In this case, the distance (d) is 510 yards and the time (t) is the remaining time after the initial 10 minutes, which is (12.5 minutes - 10.0 minutes).
Using these equations, we can calculate the initial velocity and the acceleration.
Let's calculate the initial velocity (v0) first:
Distance covered in 10 minutes = (1 mile/12.5 minutes) x (10 minutes) x (1760 yards/1 mile)
v0 = (1760 yards/12.5 minutes) x (10 minutes)
Next, we can find the acceleration:
Distance remaining = 510 yards
Time remaining = 12.5 minutes - 10.0 minutes = 2.5 minutes
Now, we can use the distance formula:
d = v0t + (1/2)at^2
510 yards = v0(2.5 minutes) + (1/2)a(2.5 minutes)^2
Substitute the value of v0 we calculated earlier:
510 yards = [(1760 yards/12.5 minutes) x (10 minutes)](2.5 minutes) + (1/2)a(2.5 minutes)^2
Simplifying the equation will give us the value of acceleration (a).