A sprinter explodes out of the starting block with an acceleration of + 2.29 m/s2, which she sustains for 1.13 s. Then, her acceleration drops to zero for the rest of the race.
To find the distance covered by the sprinter, we need to calculate the total distance during the period of acceleration and the distance during the period of constant velocity.
First, let's calculate the distance covered during the period of acceleration. We can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity is 0 m/s because the sprinter starts from rest. The acceleration is +2.29 m/s^2, and the time is 1.13 seconds. Plugging these values into the formula, we can calculate:
distance_acc = 0 * 1.13 + (1/2) * 2.29 * (1.13)^2
distance_acc = 0 + 1.2975855
distance_acc ≈ 1.30 meters (rounded to two decimal places)
So, the sprinter covers approximately 1.30 meters during the period of acceleration.
Next, let's calculate the distance covered during the period of constant velocity. Since the acceleration is zero during this period, we can use the formula:
distance = velocity * time
The final velocity during the period of acceleration is obtained by multiplying the acceleration by the time and adding it to the initial velocity:
final velocity = initial velocity + acceleration * time
final velocity = 0 + 2.29 * 1.13
final velocity ≈ 2.59 m/s (rounded to two decimal places)
Now, we can calculate the distance covered during the period of constant velocity using the formula:
distance_const_vel = velocity * time
distance_const_vel = 2.59 * (total time - acceleration time)
distance_const_vel = 2.59 * (total time - 1.13)
Since the sprinter sustains this constant velocity for the rest of the race, the total time is the time of the race minus the time of acceleration. So, if we assume the total race time is given, we can plug in the values and calculate the distance covered during the period of constant velocity.
To find the total distance, we need to sum up the distances covered during acceleration and constant velocity:
total distance = distance_acc + distance_const_vel
By following this process, you can determine the total distance covered by the sprinter.