A sprinter in a 100m race accelerates uniformly for the first 35m and then runs with constant velocity. If the sprinter's time for the first 35m is 5.4 seconds, determine his time for the race.

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written 3.5 years ago by

teamques10 ★ 68k

modified 2.7 years ago by

pedsangini276 • 4.8k

engineering mechanics

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1 Answer

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written 3.5 years ago by

teamques10 ★ 68k

Given:

u=0

t1=5.45

t2=?

speed=v=?

Solution:

(i) Acceleration motion:

$v=u+at=5.4a\rightarrow(1)$

also,

$v^2=u^2+2as=2\times a \times 35=70a\rightarrow (2)$

put (1) in (2),

$(5.4a)^2=70a\implies a=2.4m/s^2$

$\therefore v=12.96m/s$

(ii) Uniform velocity:

$x=100-35=65m;v=12.96m/s\\[2ex] \therefore t=\dfrac{x}{v}=\dfrac{65}{12.96}=5s\\[2ex] \therefore t=t_1=t_2=5.4+5=10.4s$

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