a sprinter accelerates to his maximum speed in 4 seconds . if such a sprinter finisher a 140 m race in 9 seconds what is his acceleration in the first 4 seconds
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The sprinter reached his maximum acceleration in 4secs , means there is no acceleration for the rest of the 5 secs in the 9 secs;
s = ut + 1/2 at²
Then;first you have to find the velocity for the first 4 secs = 140m/9secs
≈ 15.6 m/s
= 15.6 = 4u + 1/2 [9]² [or] 140/9 = 4u + 1/2 [9]²
= 15.6 = 4u + 0.5
= 4u = 15.6 - 0.5
= 4u = 15.056
u = 15.056/4
u = 3.76
u ≈ 4
Then ;
v² = u² + 2as
v² = [3.76]² + 2 x a x 4
v² = 14.1 + 8a
8a = v² - 14.1
a = v² - 14.1 / 8
a = v - [3.76] /4
a = v - u /t
a = 3.76 + 4a - 4 / 4
In standarad form ; the acceleration for the first 4 secs =
4a - 0.236/4
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