How Much Power Does a Cheetah Generate During Acceleration?

[triplel777]

Homework Statement

The cheetah is one of the fastest-accelerating animals, because it can go from rest to 3.4 m/s (about 8 mi/h) in 0.5 s. If its mass is 112 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in watts and horsepower.

Homework Equations

The Attempt at a Solution

v = u + at ...since the cheetah is initially at rest , u = 0 m/s therefore
v = at and we have a = (v/t)

Now power is defined as rate of doing work

P = ( Force x displacement ) / time
P = (ma x s) / t where s is the displacement s = vt
P = (m) * (v/t) (vt) divided by time t

finally doing all the algebra gives us

P = mv ^2/ t
P = (112 x 3.4^2) / 0.5
P = 2589.4

are my units wrong? but where?

 

[rl.bhat]

Displacement s = average velocity* time.
So s = vt/2

 

[mgb_phys]

Or you could simply find the change in KE and power = change in ke/time

 

[triplel777]

so would it be p= {m(v/t)(vt/2)}/t
p= 1294.7 watts

is that right?

 

[rl.bhat]

so would it be p= {m(v/t)(vt/2)}/t
p= 1294.7 watts

is that right?

No. It is only m*v^2.
Power = 1/2*m*v^2/t

 

[triplel777]

No. It is only m*v^2.
Power = 1/2*m*v^2/t

ok so 1/2*m*v^2/t
=1/2*112*3.4^2/0.5
=1294.7

is that it?

 

[rl.bhat]

Oh! Sorry. You are right.

 

[triplel777]

yup thanks so much :)

 

[DaveC426913]

Homework Statement

The cheetah is one of the fastest-accelerating animals, because it can go from rest to 3.4 m/s (about 8 mi/h) in 0.5 s.

Really? I'm pretty sure if I started with a big leap, I could hit 8mph in not much more than .5s. Is that a high acceleration?

"...a cheetah can go from 0 to 60 miles (96 kilometers) an hour in only three seconds..."
http://animals.nationalgeographic.com/animals/mammals/cheetah.html

So, 0 to 8 in the first .5s, then 8 to 60 in 2.5s.

OK, that's nearly the same slope... (8/.5 = 16) versus (52/2.5 = 20.8).