# Cheetah problem in watts

## 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.

## 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?

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rl.bhat
Homework Helper
Displacement s = average velocity* time.
So s = vt/2

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

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

is that right?

rl.bhat
Homework Helper
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

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
Homework Helper
Oh! Sorry. You are right.

yup thanks so much :)

DaveC426913
Gold Member

## 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).

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