Question

cheetahs are the fastest land animals on earth. it’s estimated they can run with a speed of $30\frac{\text{m}}{\text{s}} \left( \text{about } 70\frac{\text{mi}}{\text{h}} \
ight)$ or higher!
image of a cheetah running
not only can cheetahs run with high speed, but they can accelerate quickly from rest.
if a cheetah begins at rest and begins running with an acceleration of $10\frac{\text{m}}{\text{s}^2}$, how long will it take her to reach a speed of $30\frac{\text{m}}{\text{s}}$?
blank seconds
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Explanation:

Step1: Recall the acceleration formula

The formula relating initial velocity (\(v_0\)), final velocity (\(v\)), acceleration (\(a\)), and time (\(t\)) is \(v = v_0+at\). Since the cheetah starts from rest, \(v_0 = 0\space\frac{\text{m}}{\text{s}}\).

Step2: Substitute known values into the formula

We know \(v = 30\space\frac{\text{m}}{\text{s}}\), \(v_0 = 0\space\frac{\text{m}}{\text{s}}\), and \(a = 10\space\frac{\text{m}}{\text{s}^2}\). Substituting into \(v = v_0+at\), we get \(30 = 0 + 10t\).

Step3: Solve for \(t\)

To solve for \(t\), divide both sides of the equation \(30 = 10t\) by 10. So, \(t=\frac{30}{10}=3\).

Answer:

3