Math / Algebra

QuestionA car accelerates from rest at $4.4 \mathrm{~m} / \mathrm{s}^{2}$ . How much time does it need to attain a speed of $5 \mathrm{~m} / \mathrm{s}$ ?
Answer in units of s. Answer in units of s.

Studdy Solution

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: $t = \frac{5 \mathrm{~m} / \mathrm{s}}{4.4 \mathrm{~m} / \mathrm{s}^{2}}$ $t \approx 1.136 \mathrm{~s}$

STEP 9

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

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QuestionA car accelerates from rest at $4.4 \mathrm{~m} / \mathrm{s}^{2}$ . How much time does it need to attain a speed of $5 \mathrm{~m} / \mathrm{s}$ ?
Answer in units of s. Answer in units of s.

Studdy Solution

STEP 1

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

STEP 7

STEP 8

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

STEP 9

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

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QuestionA car accelerates from rest at 4.4 m/s24.4 \mathrm{~m} / \mathrm{s}^{2}4.4 m/s2. How much time does it need to attain a speed of 5 m/s5 \mathrm{~m} / \mathrm{s}5 m/s ?Answer in units of s. Answer in units of s.

Studdy Solution

STEP 1

STEP 2

1. Define Acceleration2. Calculate the Time

STEP 3

Alright, so we know the car is accelerating at 4.4 m/s24.4 \mathrm{~m} / \mathrm{s}^{2}4.4 m/s2.But what does that *really* mean?It means that every second, the car's speed increases by 4.4 m/s4.4 \mathrm{~m} / \mathrm{s}4.4 m/s.That's our **rate of change**!

STEP 4

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

STEP 5

Let's use variables to make things easier.Let aaa represent acceleration, vfv_fvf​ represent the **final speed**, viv_ivi​ represent the **initial speed**, and ttt represent the time.So, we have: a=vf−vita = \frac{v_f - v_i}{t}a=tvf​−vi​​

STEP 6

STEP 7

STEP 8

Let's **crunch the numbers**: t=5 m/s4.4 m/s2t = \frac{5 \mathrm{~m} / \mathrm{s}}{4.4 \mathrm{~m} / \mathrm{s}^{2}}t=4.4 m/s25 m/s​ t≈1.136 st \approx 1.136 \mathrm{~s}t≈1.136 s

STEP 9

So, it takes approximately 1.1361.1361.136 seconds for the car to reach a speed of 5 m/s5 \mathrm{~m} / \mathrm{s}5 m/s.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA car accelerates from rest at $4.4 \mathrm{~m} / \mathrm{s}^{2}$ . How much time does it need to attain a speed of $5 \mathrm{~m} / \mathrm{s}$ ?
Answer in units of s. Answer in units of s.

1. Define Acceleration
2. Calculate the Time

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!

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

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: $a = \frac{v_f - v_i}{t}$

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 $5 \mathrm{~m} / \mathrm{s}$ .