Jennifer is running the 100.0 m dash at track. She accelerates at a rate of 0.88 m/s2 for the first 45 m and then maintains this speed for the remainder of the race. How long will it take her to finish the race?
d1 = 0.5a*T1^2 = 45 m. Solve for T1.
0.5*0.88*T1^2 = 45.
T1^2 = 102.3
T1 = 10.11 s. to run the 1st 45 m.
V = a*T1 = 0.88*10.11 = 8.9 m/s.
d2 = V*T2 = 8.9 * T2 = 100-45 = 55 m.
T2 = 55/8.9 = 6.18 s. To run the last 55
m.
T = T1+T2 = 10.11 + 6.18 = 16.29 s. to
run the race.
To find the time it will take for Jennifer to finish the race, we need to consider two parts of her motion: the acceleration phase and the constant speed phase.
In the acceleration phase, Jennifer is accelerating at a rate of 0.88 m/s^2 for the first 45 m. To find the time it takes for Jennifer to reach this distance, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since Jennifer starts from rest (initial velocity = 0) and we're solving for time, the formula simplifies to:
45 m = 0.5 * 0.88 m/s^2 * t^2
We can rearrange the equation to solve for t:
t^2 = (2 * 45 m) / 0.88 m/s^2
t^2 = 102.27 s^2
Taking the square root of both sides, we find:
t ≈ 10.11 s
So, it will take Jennifer approximately 10.11 seconds to reach the 45 m mark.
In the constant speed phase, Jennifer is maintaining the same speed for the remainder of the race. Since she runs at a constant speed after reaching 45 m, the distance traveled in this phase is:
remaining distance = total distance - distance in the acceleration phase
remaining distance = 100 m - 45 m
remaining distance = 55 m
To find the time it takes for Jennifer to cover this remaining distance at a constant speed, we can use the formula:
time = distance / speed
In this case, Jennifer's speed during the constant speed phase is the same as her speed at the end of the acceleration phase. We can find this speed by multiplying her acceleration by the time taken to reach the 45 m mark:
speed = acceleration * time
speed = 0.88 m/s^2 * 10.11 s
speed ≈ 8.91 m/s
Now, we can calculate the time it takes for Jennifer to cover the remaining distance:
time = 55 m / 8.91 m/s
time ≈ 6.18 s
Therefore, it will take Jennifer approximately 6.18 seconds to cover the remaining 55 meters.
Finally, to find the total time it will take Jennifer to finish the race, we add the time taken in the acceleration phase to the time taken in the constant speed phase:
total time = time in acceleration phase + time in constant speed phase
total time ≈ 10.11 s + 6.18 s
total time ≈ 16.29 s
So, it will take Jennifer approximately 16.29 seconds to finish the race.