Aworld record was set for the men's 100-m dash in the 2008 olympic games in beijing by usain bolt of jamaica. bolt "coasted" across the finish line with a time of 9.69 s. if we assume that bolt accelerated for 3.00 s to reach his maximum speed, and maintained that speed for the rest of the race, (a) calculate his maximum speed and (b) his acceleration. ans: (a) 12.2 m/s, (b) 4.07 m/s2

Usain Bolt's acceleration  is 4.07 m/s² for the first 3.00 s and his maximum velocity is 12.2 m/s.

Bolt  starts from rest and accelerates with an acceleration a for a time t₁ =3.00 s and at the end of this time, he reaches a speed v. He travels a distance s₁ during this time.

Therefore,

His final velocity at the end of time t₁ is given by,

He travels a further distance s₂ with a constant velocity v for a time t₂. Therefore,

From equation (2),

......(3)

The total distance traveled is s =100 m and

From equations (1) and (3)

write an expression for a.

The total time taken to complete the race is 9.69 s, therefore,

Substitute 100 m for s, 3.00 s for t₁ and 6.69 s for  t₂ and calculate the acceleration.

In equation (2) substitute 4.07 m/s²for a and 3.00 s for t₁ .

The maximum velocity of Usain Bolt is 12.2 m/s and his acceleration is 4.07m/s².

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas