Question

hw
general equations:
uam equations:

1. noah lyles the us olympic runner accelerates at 4.2 m/sec/sec for 9.76 seconds before winning his race. what event (how far) did noah lyles run?

step 1: identify variables
4.2m/sec² = a
9.76sec = t
step 2: identify equation
δd = vᵢt+1/2at²
step 3: calculate answer with units

1. a car accelerates at a rate of 3.0 m/s². if its original speed is 8.0 m/s, how many seconds will it take the car to reach a final speed of 25.0 m/s?

step 1: identify variables
3.0m/s² = a
8.0m/s = vᵢ
step 2: identify equation
step 3: calculate answer with units

1. a ball free falls from the top of the roof for 5 seconds.

a. how far did the ball fall?
step 1: identify variables
step 2: identify equation
step 3: calculate answer with units
b. what was the velocity of the ball at 5 seconds?
step 1: identify variables
step 2: identify equation
step 3: calculate answer with units

1. how much time would it take for thunder to travel 1500 meters if it has a speed of 330 meters/second?

step 1: identify variables
step 2: identify equation
step 3: calculate answer with units

Explanation:

1.

Step1: Identify variables

The acceleration $a = 4.2\ m/s^{2}$, the time $t=9.76\ s$, and the initial - velocity $v_{i}=0\ m/s$ (assuming starting from rest).

Step2: Identify equation

We use the equation $\Delta d=v_{i}t+\frac{1}{2}at^{2}$. Since $v_{i} = 0$, the equation simplifies to $\Delta d=\frac{1}{2}at^{2}$.

Step3: Calculate answer with units

Substitute $a = 4.2\ m/s^{2}$ and $t = 9.76\ s$ into the equation:
\[

$$\begin{align*} \Delta d&=\frac{1}{2}\times4.2\ m/s^{2}\times(9.76\ s)^{2}\\ &=2.1\ m/s^{2}\times95.2576\ s^{2}\\ &=200.04096\ m\approx200\ m \end{align*}$$

\]

Step1: Identify variables

The acceleration $a = 3.0\ m/s^{2}$, the initial - velocity $v_{i}=8.0\ m/s$, and the final - velocity $v_{f}=25.0\ m/s$.

Step2: Identify equation

We use the equation $v_{f}=v_{i}+at$, and we want to solve for $t$. Rearranging the equation gives $t=\frac{v_{f}-v_{i}}{a}$.

Step3: Calculate answer with units

Substitute $v_{f}=25.0\ m/s$, $v_{i}=8.0\ m/s$, and $a = 3.0\ m/s^{2}$ into the equation:
\[

$$\begin{align*} t&=\frac{25.0\ m/s - 8.0\ m/s}{3.0\ m/s^{2}}\\ &=\frac{17.0\ m/s}{3.0\ m/s^{2}}\\ &\approx5.67\ s \end{align*}$$

\]

Step1: Identify variables

The acceleration due to gravity $a = g=9.8\ m/s^{2}$ (near the Earth's surface), the initial - velocity $v_{i}=0\ m/s$ (starting from rest), and the time $t = 5\ s$.

Step2: Identify equation

We use the equation $\Delta d=v_{i}t+\frac{1}{2}at^{2}$. Since $v_{i}=0$, the equation simplifies to $\Delta d=\frac{1}{2}at^{2}$.

Step3: Calculate answer with units

Substitute $a = 9.8\ m/s^{2}$ and $t = 5\ s$ into the equation:
\[

$$\begin{align*} \Delta d&=\frac{1}{2}\times9.8\ m/s^{2}\times(5\ s)^{2}\\ &=4.9\ m/s^{2}\times25\ s^{2}\\ &=122.5\ m \end{align*}$$

\]

Answer:

$200\ m$

2.