very difficult the ans found here wrong
A sprinter runs a 100 m dash in 12.0 s. She starts from rest
with a constant acceleration ax for 3.0 s and then runs with constant
speed for the remainder of the race. What is the value of ax?
Homework Answers
SOLUTION :
!00m completed in 12 sec.
Initial speed = 0 m/s
Run for 3 sec at constant acceleration ax and then runs at constant speed.
Speed after 3 sec = ax * 3 = 3 ax m/s
Average speed during first 3 sec of acceleration = (3 ax + 0)/2 = 1.5 ax m/s
So, we can consider run of 3 sec. at average speed of 1.5 ax m/s and remaining 9 sec at the speed of 9 sec.
So,
Distance run in 12 sec = 1.5 ax * 3 + 3.0 ax * 9
=> 100 = 4.5 ax + 27 ax
=> 100 = 31.5 ax
=> ax = 100/31.5
=> ax = 3.1746 m/s^2 = 3.175 m/s^2 approx. (ANSWER).
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