Question

how to solve equation - based problems
every time you solve a problem, use these same steps:

• write the equation being used.
• rearrange the equation if needed, based on what you are solving for.
• convert any units, if needed, so that all units are compatible.
• plug in the numbers you were given, with all units
• solve for the answer, with correct units.

acceleration practice
problem 1: a fox goes hunting in the forest and spots a mouse. the mouse is running at a speed of 0.5 m/s and accelerates to a speed of 1.4 m/s in 5 seconds. the fox started at a speed of 0.8 m/s and accelerated to a top speed of 1.8 m/s in 9 seconds. which animal has the faster acceleration in this scenario?
problem 2: a car starts from rest and accelerates at a constant rate of 2 m/s². after reaching a speed of 39 m/s, how much time has passed?
problem 3: daniel is driving his car at a speed of 41 miles per hour. he then accelerates at 0.1 miles/hour² for 0.017 hours to make this change in speed. now how fast is he driving?

Explanation:

Step1: Recall acceleration formula

The formula for acceleration is $a=\frac{v_f - v_i}{t}$, where $a$ is acceleration, $v_f$ is final - velocity, $v_i$ is initial - velocity, and $t$ is time.

Step2: Calculate mouse's acceleration

For the mouse, $v_i = 0.5\ m/s$, $v_f=1.4\ m/s$, and $t = 5\ s$.
$a_{mouse}=\frac{1.4 - 0.5}{5}=\frac{0.9}{5}=0.18\ m/s^{2}$

Step3: Calculate fox's acceleration

For the fox, $v_i = 0.8\ m/s$, $v_f = 1.8\ m/s$, and $t = 9\ s$.
$a_{fox}=\frac{1.8 - 0.8}{9}=\frac{1}{9}\approx0.11\ m/s^{2}$
Since $0.18>0.11$, the mouse has a faster acceleration.

Step4: Solve Problem 2

We use the formula $a=\frac{v_f - v_i}{t}$, and we want to find $t$. Rearranging for $t$ gives $t=\frac{v_f - v_i}{a}$. The car starts from rest, so $v_i = 0\ m/s$, $v_f = 39\ m/s$, and $a = 2\ m/s^{2}$.
$t=\frac{39 - 0}{2}=19.5\ s$

Step5: Solve Problem 3

We use the formula $v_f=v_i+at$. Here, $v_i = 41\ miles/hour$, $a = 0.1\ miles/hour^{2}$, and $t = 0.017\ hours$.
$v_f=41+0.1\times0.017=41 + 0.0017=41.0017\ miles/hour$

Answer:

Problem 1: The mouse has the faster acceleration.
Problem 2: 19.5 s
Problem 3: 41.0017 miles/hour