Math Snap

STEP 1

What is this asking?
How long does it take a car starting from a standstill to reach a speed of $5 \mathrm{~m} / \mathrm{s}$ if it's accelerating at $4.4 \mathrm{~m} / \mathrm{s}^{2}$?
Watch out!
Don't mix up speed and acceleration; acceleration is how quickly the speed changes!
Also, remember that the car starts from rest, meaning its initial speed is $0 \mathrm{~m} / \mathrm{s}$.

STEP 2

1. Define Acceleration
2. Calculate the Time

STEP 3

Alright, so we know the car is accelerating at $4.4 \mathrm{~m} / \mathrm{s}^{2}$.
But what does that really mean?
It means that every second, the car's speed increases by $4.4 \mathrm{~m} / \mathrm{s}$.
That's our rate of change!

STEP 4

We can write this mathematically using the formula for acceleration:
$$\text{Acceleration} = \frac{\text{Change in Speed}}{\text{Change in Time}}$$

STEP 5

Let's use variables to make things easier.
Let $a$ represent acceleration, $v_f$ represent the final speed, $v_i$ represent the initial speed, and $t$ represent the time.
So, we have:
$$a = \frac{v_f - v_i}{t}$$

STEP 6

We're trying to find the time $t$, so let's rearrange the formula to solve for it.
We can do this by multiplying both sides of the equation by $t$ and then dividing both sides by $a$:
$$t \cdot a = \frac{v_f - v_i}{t} \cdot t$$ $$t \cdot a = v_f - v_i$$$$\frac{t \cdot a}{a} = \frac{v_f - v_i}{a}$$$$t = \frac{v_f - v_i}{a}$$

STEP 7

Now we can plug in the values we know.
The final speed $v_f$ is $5 \mathrm{~m} / \mathrm{s}$, the initial speed $v_i$ is $0 \mathrm{~m} / \mathrm{s}$ (because the car starts from rest!), and the acceleration $a$ is $4.4 \mathrm{~m} / \mathrm{s}^{2}$.
$$t = \frac{5 \mathrm{~m} / \mathrm{s} - 0 \mathrm{~m} / \mathrm{s}}{4.4 \mathrm{~m} / \mathrm{s}^{2}}$$

STEP 8

Let's crunch the numbers:
$$t = \frac{5 \mathrm{~m} / \mathrm{s}}{4.4 \mathrm{~m} / \mathrm{s}^{2}}$$ $$t \approx 1.136 \mathrm{~s}$$

So, it takes approximately $1.136$ seconds for the car to reach a speed of $5 \mathrm{~m} / \mathrm{s}$.