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In asian games for 100 m event an athlete accelerates uniformly from the start to his maximum velocity in a distance of 4m & runs the remaining distance with that velocity.

If the athlete finishes the race in 10.4sec, determine: (i) his initial acceleration; (ii) his maximum velocity.

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Let t1 be time in which athlete achieves max. Velocity & let t2 be the remaining time

Let v be the maximum velocity achieved bt athlete & a be his acceleration

So,t1+t2=10.4____(i)

Also for uniformly acc. Motion , we get

4=(1/2)a(t1)2____(ii)  &  v=a(t1)_____(iii)

For uniform velocity motion

96=v(t2)______(iv)

Putting eqn(iii) in eqn(iv)

96=a(t1)(t2)____(v)

Putting value of a from eqn (ii) & value of t2 from eqn (i) in eqn (v)

96=[8/(t1)2](t1)(10.4t1)96(t1)=83.28(t1)

So, we get, t1=0.8sec & t2=9.6sec

Putting t1 & t2 in eqn (iv) & (v),we get

a=12.5m/s2 & v=10m/s

His initial acceleration is 12.5m/s2 & his maximum velocity is 10 m/s

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