Question

A cheetah, the fastest of all land animals over a short distance, accelerates from rest to 26m/s. Assuming that the acceleration is constant, find the average speed of the cheetah

Answer 1

If acceleration is constant, then velocity grows linearly and you can take average of initial and final velocities.

Answer 2

Yep. You can verify it using definition of average velocity = total distance ÷ total time.
The total distance, x=0.5(a)(t)^2, where 'a' is the constant acceleration and 't' is the time.
You can make up whatever number you want for 't' and find 'a' by (final velocity) ÷ (total time).

Answer 3

i do not see a "total distance" in the question

Answer 4

@amistre64 q.v. "You can make up whatever number you want for 't' and find 'a' by (final velocity) ÷ (total time)."

Answer 5

im just not sure how we can come up with a definitive solution with the information given.

Answer 6

e.g. Let t = 3s.
a = 26m/s ÷ 3s ≈ 8.67m/s/s.
x = (0.5)(8.67m/s/s)(3s)^2 = 39m.
average velocity = 39m/3s = 13m/s.

Answer 7

or average velocity = (final v - initial v)/2. [because the velocity increase is linear].

Answer 8

ok, thats starting to make better sense to me now

Answer 9

We have initial velocity, final velocity, and the fact that acceleration is constant. That is plenty of information.

Answer 10

I hate aww snap.

Answer 11

the average of the instantaneous velocities .... i was reading it askew :)

Answer 12

OK, so we need \(t\) right now.\[v^2 = u^2 + 2as\]We could've calculated the acceleration through the formula we already know.

Answer 13

Then we had one variable to solve for: s(or the distance).

Answer 14

After solving for s, we count have found s/t which is the speed.

Answer 15

How do you get s without a? You need t to find a. If you already have t and a, you can get s with s=.5at^2. (The fundamental kinematics formula).

Answer 16

Or... you can just do (final - initial)/2.