Question

Researchers have measured the acceleration of racing greyhounds as a function of their speed; a simplified version of their results is shown in (Figure 1). The acceleration at low speeds is constant and is limited by the fact that any greater acceleration would result in the dog pitching forward because of the force acting on its hind legs during its power stroke. At higher speeds, the dog's acceleration is limited by the maximum power its muscles can provide.
How far does the dog run until its speed reaches 4.0 m/s?

Answer 1

$\Huge\boxed{\boxed{\dfrac{4}{5}\ \text{meters}}}$

Let's start by finding the time it takes for the dog to reach a velocity of $4$ m/s.

We can use the following equation, where $v_i$ is initial velocity, $v_f$ is final velocity, $t$ is time, and $a$ is acceleration.

$v_f-v_i=at$

We're trying to solve for $t$ first, so divide both sides by $a$.

$\dfrac{v_f-v_i}{a}=t$

Substitute in the known values.

$\dfrac{4-0}{10}=t$

$\dfrac{4}{10}=t$

$\dfrac{2}{5}=t$

Now, we can use the following formula to find the distance.

$s=v_it+\dfrac{1}{2}at^2$

Substitute in the known values.

$s=0*\dfrac{2}{5}+\dfrac{1}{2}*10*(\frac{2}{5})^2$

Anything multiplied by $0$ is

$s=\dfrac{1}{2}*10*(\frac{2}{5})^2$

Just simplify from there.

$s=\dfrac{1}{2}*10*\dfrac{4}{25}$

$s=5*\dfrac{4}{25}$

$s=\dfrac{20}{25}$

$s=\boxed{\dfrac{4}{5}}$

Answer 2

Hey there!

The hind legs of the dog create it to accelerate.

We know the mass of the dog is 36km (m).

We know that the acceleration of the dog it 10m/s² (a).

Find the average force with the formula [ f = ma ] where m = mass and a = acceleration.

f = 36*10

f = 360 newtons

We don't know the traveled distance but we do know that the starting speed of the dog was 0m/s and the ending speed was 4m/s.

We can use the formula [ vf² = vo² + 2ad ] where vf = final speed, vo = starting speed, a = acceleration, and d = distance.

We know all the variables except the distance, so we are going to solve for d.

(4)² = (0)² + 2(10)(d)

16 = 0 + 20d

16 = 20d

16/20 = 20d/20

0.8 = d

Therefore, the dog runs 0.8 meters until it reaches 4m/s.

Best of Luck!