A runner, beginning at rest, completed a 50 m run with a final speed of 6 m/s. Assuming constant acceleration.
a) What was the average speed of the runner?
b) What was the runner's time?
c) What was the acceleration?
a) half the final speed
b) distance/(average speed)
c) (final speed)/(elapsed tme)
= (final speed/([distance/average speed)]
=(final speed)^2/[2*(distance)]
To find the answers to the given questions, we can use the formulas and steps you have provided. Let's break it down step by step:
a) Average speed:
The average speed of an object is given by the formula: average speed = total distance ÷ total time
In this case, the total distance is 50 m and the total time is the time it takes to complete the run.
Since we know the final speed and assuming constant acceleration, we can use a formula that relates final speed, initial speed (which is 0 in this case), and acceleration: final speed = initial speed + (acceleration × time).
Since the initial speed is 0, the formula simplifies to: final speed = acceleration × time.
Rearranging the formula gives us: time = final speed ÷ acceleration.
Plugging in the given values:
average speed = total distance ÷ total time
average speed = 50 m ÷ (final speed ÷ acceleration)
average speed = 50 m ÷ (6 m/s ÷ acceleration)
average speed = 50 m × (acceleration ÷ 6 m/s)
average speed = 8.33 × acceleration
So, the average speed of the runner is 8.33 times the acceleration.
b) Time:
We already know that time = final speed ÷ acceleration.
Plugging in the given values:
time = 6 m/s ÷ acceleration
So, the time taken by the runner is 6 divided by the acceleration.
c) Acceleration:
We can solve for acceleration by rearranging the formula mentioned earlier:
final speed = acceleration × time
acceleration = final speed ÷ time
Plugging in the given values:
acceleration = 6 m/s ÷ (6 m/s ÷ acceleration)
acceleration = 6 m/s ÷ (6 ÷ acceleration)
acceleration = 6 × (acceleration ÷ 6)
acceleration = acceleration
So, the acceleration of the runner is equal to the acceleration itself.
To summarize:
a) The average speed of the runner is 8.33 times the acceleration.
b) The time taken by the runner is 6 divided by the acceleration.
c) The acceleration of the runner is equal to the acceleration itself.