Question

1. Deshaun Watson (100 kg) accelerates from rest to 9.0 m/s in 1.5 s. What is the average power

output of Deshaun in kW? (2 mark)

Answer 1

P = 5400[W]

Step-by-step explanation:

We must use the following equation of kinematics to calculate the acceleration.

`v_(f)=v_(o)+a*t`

where:

Vf = final velocity = 9 [m/s]

Vo = initial velocity = 0 (starting from rest)

a = acceleration [m/s²]

t = time = 1.5 [s]

`9=0+a*1.5\\a=9/1.5\\a=6[m/s^(2) ]`

Now with this second equation of kinematics, we can determine the distance traveled.

`v_(f)^(2)=v_(o)^(2)+2*a*x`

where:

x= distance [m]

`9^(2) = 0 +2*6*x\\12*x=81\\x=6.75[m]`

Now we must use Newton's second law which tells us that the sum of forces is equal to the product of mass by acceleration.

∑F = m*a

Now replacing:

`F=100*6\\F=600[N]`

Ahora la potencia se puede calcular por medio del producto de la fuerza por velocidad.

`P=F*v`

where:

P = power [W]

F = force = 600 [N]

v = velocity = 9 [m/s]

`P=9*600\\P=5400[W]`