A sprinter accelerates at 4 m/s2 for 3 seconds, and then runs the rest of the race at a constant speed. If the race is 100 m, how much time does the sprinter take to fi�nish the race?
1/2(acceleration)(time^2)=distance
1/2(4 m/s^2)(3s)^2= 18m
100m-18m= 82m (total distance remaining)
Time= Distance/speed
Time= 82m/12m/s = 6.83s
Time= 6.83s + 3s= 9.83s
To answer this question, we need to calculate the time it takes for the sprinter to reach their constant speed and then calculate the time it takes for them to run the remaining distance at that constant speed.
Step 1: Calculate the time it takes for the sprinter to reach their constant speed.
The sprinter accelerates at a rate of 4 m/s^2 for 3 seconds. We can use the formula: time = velocity / acceleration.
Acceleration = 4 m/s^2
Time = 3 seconds
Substituting these values into the formula:
Time = 3 s
Step 2: Calculate the remaining distance the sprinter runs at a constant speed.
The total distance of the race is given as 100 m. The distance covered during the acceleration phase can be calculated using the formula: distance = 1/2 × acceleration × time^2.
Acceleration = 4 m/s^2
Time = 3 seconds
Substituting these values into the formula:
Distance = 1/2 × 4 m/s^2 × (3 s)^2
Distance = 1/2 × 4 m/s^2 × 9 s^2
Distance = 18 m
The remaining distance the sprinter runs at a constant speed is:
Remaining distance = Total distance - Distance during acceleration
Remaining distance = 100 m - 18 m
Remaining distance = 82 m
Step 3: Calculate the time it takes the sprinter to run the remaining distance at a constant speed.
We can use the formula: time = distance / speed.
Distance = 82 m
Time = Distance / Speed
Substituting these values into the formula:
Time = 82 m / Speed
Since the speed of the sprinter during the constant speed phase is not given, we cannot calculate the exact time it takes.
To solve this problem, we need to find the time it takes for the sprinter to finish the race.
First, let's calculate the distance covered during acceleration. We can use the formula:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
Since the initial velocity is 0 m/s (as the sprinter starts from rest), the formula becomes:
Distance = (1/2) * Acceleration * Time^2
Substituting the given values:
Distance = (1/2) * 4 m/s^2 * (3s)^2
Distance = 6 * 4 m
Distance = 24 m
So, the sprinter covers 24 meters during the acceleration phase.
Now, let's calculate the remaining distance that the sprinter has to cover at a constant speed.
Remaining Distance = Total Distance - Distance during acceleration
Remaining Distance = 100 m - 24 m
Remaining Distance = 76 m
Finally, to find the time it takes to cover the remaining distance, we can use the formula:
Time = Distance / Speed
Since the remaining distance is 76 meters and the sprinter runs at a constant speed, we need to know the speed. However, it isn't provided in the question. Please provide the constant speed at which the sprinter runs, so we can calculate the final time.