Question

The infamous chicken is dashing toward home plate with a speed of 5.8m/s when he decides to hit the dirt. The chicken slides for 1.1s, just reaching the plate as he stops. (safe of course). (a) What is the magnitude of the chickens acceleration (b) How far did the chicken slide?

Answer 1

We know that

• The initial speed is 5.8 m/s.

,

• The time elapsed is 1.1 seconds.

,

• The final speed is zero because it will stop.

Let's find the acceleration. We have to use a formula that involves the initial speed, the time spent, the final speed, and acceleration.

`v_f=v_0+at`

Now we use the given magnitudes to solve for a.

`\begin{gathered} 0=5.8\cdot(m)/(s)+a\cdot1.1\sec \\ -5.8\cdot(m)/(s)=a\cdot1.1\sec \\ a=(-5.8\cdot(m)/(s))/(1.1\sec ) \\ a\approx-5.3\cdot(m)/(s^2) \end{gathered}`

(a) The magnitude of the chicken's acceleration is -5.3 m/s^2.

Now, to find how far the chicken slid, we have to use a formula that includes distance.

`v^2_f=v^2_0+2ad`

Let's use the magnitudes we know to find d.

`\begin{gathered} 0=(5.8\cdot(m)/(s))^2+2(-5.3\cdot(m)/(s^2))d \\ 0=33.64\cdot(m^2)/(s^2)-10.6\cdot(m)/(s^2)\cdot d \\ d=(-33.64\cdot(m^2)/(s^2))/(-10.6\cdot(m)/(s^2)) \\ d\approx3.2m \end{gathered}`

(b) The chicken slid 3.2 meters.

As you can observe, the positive direction of the movement is towards the home plate. So, the acceleration is towards the third base because it's negative, that is, the chicken is slowing down to get to home plate.

Therefore, the direction of the acceleration is towards the third base.