In a 100m race, Maggie and Judy cross the finish line in a dead heat, both taking 11.4s. Accelerating uniformly, Maggie took 1.80s and Judy 2.95s to attain maximum speed, which they maintained for the rest of the race. What was Maggie's acceleration?
To find Maggie's acceleration, we need to use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Since Maggie took 1.80s to attain maximum speed, we can consider this as her acceleration phase. During this phase, her initial velocity would be 0 m/s, and her final velocity is the maximum speed she attained.
Since both Maggie and Judy crossed the finish line in a dead heat, it means they both traveled the same distance of 100m. Therefore, we can use this information to find their maximum speeds using the formula:
speed = distance / time
For Maggie:
initial velocity = 0 m/s
distance = 100m (since she covered the same distance as Judy)
To find Maggie's maximum speed, we divide the distance (100m) by the time (1.80s):
Maggie's maximum speed = 100m / 1.80s
Now that we have Maggie's maximum speed, we can use the formula for acceleration to find her acceleration. The final velocity in this case is Maggie's maximum speed, and the time is the acceleration phase time (1.80s).
acceleration = (final velocity - initial velocity) / time
acceleration = (Maggie's maximum speed - 0m/s) / 1.80s
So, to find Maggie's acceleration, we divide the maximum speed (100m / 1.80s) by the time taken to reach that speed (1.80s).