Acceleration Problems: 1. Acceleration is the rate at which what changes? Velocity 2. What is the acceleration of a car moving in a straight-line path that travels at constant speed of $$ 100 \mathrm{~km} / \mathrm{h} $$ ? $$ a=0 \mathrm{~m} / \mathrm{s}^{2} $$ 3. What is the acceleration of a car moving in a straight-line path that increases it speed from rest to $$ 100 \mathrm{~km} / \mathrm{h} $$ in 0.2 hrs ? $$ 0.0586 \mathrm{~m} / \mathrm{s}^{2} $$ 4. Light travels in a straight line at a constant speed of $$ 300,000 \mathrm{~km} / \mathrm{s} $$. What would the acceleration of light 3 seconds later? $$ 0 \mathrm{~m} / \mathrm{s}^{2} $$ 5. A dragster going at $$ 15 \mathrm{~m} / \mathrm{s} $$ north increases its velocity to $$ 25 \mathrm{~m} / \mathrm{s} $$ north in 4 seconds. What's its acceleration during that time interval? $$ 2.3 \mathrm{~m} / \mathrm{s}^{2} $$ 6. A car going $$ 30 \mathrm{~m} / \mathrm{s} $$ undergoes an acceleration of $$ 2 \mathrm{~m} / \mathrm{s}^{2} $$ for 4 seconds. What is its final speed? $$ 38 \mathrm{~m} / \mathrm{s} $$ 7. A man on a unicycle pedals for 2 seconds at a speed of $$ 6 \mathrm{~m} / \mathrm{s} $$ and then pedals another 2 seconds at a rate of $$ 6 \mathrm{~m} / \mathrm{s} $$. What is the acceleration of the cyclist? $$ 0 \mathrm{~m} / \mathrm{s}^{2} $$ 8. If a Porsche accelerates at a rate of $$ 25 \mathrm{~km} / \mathrm{h}^{*} \mathrm{~s} $$ and goes from rest to $$ 125 \mathrm{~km} / \mathrm{hr} $$. How long did it take the car to reach its final speed? 5 seconas 9. If a car is traveling at $$ 35 \mathrm{~m} / \mathrm{s} $$ and the driver sees a deer and slams on her brakes to come to stop in 5 seconds, what is her rate of acceleration? $$ -7 \mathrm{mi} \mathrm{s}^{2} $$ 10. A rocket decelerates at a rate of $$ 5 \mathrm{~m} / \mathrm{s}^{2} $$. If the initial velocity of the rocket was $$ 200 \mathrm{~m} / \mathrm{s} $$, how fast would the rocket be traveling 20 seconds later? How long will it take before the rocket . comes to a stop? Uo seconde Acceleration Calculations

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Let's go through the acceleration problems step by step, extracting the known conditions and providing detailed solutions.

### 1. Acceleration Definition
- **Acceleration** is the rate at which **velocity** changes.

### 2. Constant Speed
- A car moving at a constant speed of $$ 100 \mathrm{~km/h} $$ has an acceleration of:
$$
a = 0 \mathrm{~m/s}^2
$$
This is because there is no change in velocity.

### 3. Acceleration from Rest
- A car increases its speed from rest to $$ 100 \mathrm{~km/h} $$ in $$ 0.2 $$ hours. First, we convert $$ 100 \mathrm{~km/h} $$ to $$ \mathrm{m/s} $$:
$$
100 \mathrm{~km/h} = \frac{100 \times 1000 \mathrm{~m}}{3600 \mathrm{~s}} \approx 27.78 \mathrm{~m/s}
$$
Now, the acceleration $$ a $$ can be calculated using the formula:
$$
a = \frac{\Delta v}{\Delta t} = \frac{27.78 \mathrm{~m/s} - 0 \mathrm{~m/s}}{0.2 \times 3600 \mathrm{~s}} = \frac{27.78 \mathrm{~m/s}}{720 \mathrm{~s}} \approx 0.0386 \mathrm{~m/s}^2
$$

### 4. Acceleration of Light
- Light travels at a constant speed of $$ 300,000 \mathrm{~km/s} $$. Therefore, the acceleration after 3 seconds is:
$$
a = 0 \mathrm{~m/s}^2
$$

### 5. Dragster Acceleration
- A dragster increases its velocity from $$ 15 \mathrm{~m/s} $$ to $$ 25 \mathrm{~m/s} $$ in $$ 4 $$ seconds. The acceleration is:
$$
a = \frac{25 \mathrm{~m/s} - 15 \mathrm{~m/s}}{4 \mathrm{~s}} = \frac{10 \mathrm{~m/s}}{4 \mathrm{~s}} = 2.5 \mathrm{~m/s}^2
$$

### 6. Final Speed of a Car
- A car going $$ 30 \mathrm{~m/s} $$ accelerates at $$ 2 \mathrm{~m/s}^2 $$ for $$ 4 $$ seconds. The final speed $$ v_f $$ is:
$$
v_f = v_i + a \cdot t = 30 \mathrm{~m/s} + (2 \mathrm{~m/s}^2 \cdot 4 \mathrm{~s}) = 30 \mathrm{~m/s} + 8 \mathrm{~m/s} = 38 \mathrm{~m/s}
$$

### 7. Cyclist Acceleration
- The cyclist pedals at a constant speed of $$ 6 \mathrm{~m/s} $$ for $$ 4 $$ seconds. Therefore, the acceleration is:
$$
a = 0 \mathrm{~m/s}^2
$$

### 8. Time to Reach Final Speed
- A Porsche accelerates at $$ 25 \mathrm{~km/h/s} $$ from rest to $$ 125 \mathrm{~km/h} $$. First, convert $$ 125 \mathrm{~km/h} $$ to $$ \mathrm{m/s} $$:
$$
125 \mathrm{~km/h} = \frac{125 \times 1000 \mathrm{~m}}{3600 \mathrm{~s}} \approx 34.72 \mathrm{~m/s}
$$
Now, using the acceleration:
$$
t = \frac{\Delta v}{a} = \frac{34.72 \mathrm{~m/s}}{(25 \mathrm{~km/h/s} \cdot \frac{1 \mathrm{~h}}{3600 \mathrm{~s}})} \approx 5 \mathrm{s}
$$

### 9. Rate of Acceleration
- A car traveling at $$ 35 \mathrm{~m/s} $$ comes to a stop in $$ 5 $$ seconds. The acceleration is:
$$
a = \frac{0 \mathrm{~m/s} - 35 \mathrm{~m/s}}{5 \mathrm{s}} = \frac{-35 \mathrm{~m/s}}{5 \mathrm{s}} = -7 \mathrm{~m/s}^2
$$

### 10. Rocket Deceleration
- A rocket decelerates at $$ 5 \mathrm{~m/s}^2 $$ from an initial velocity of $$ 200 \mathrm{~m/s} $$. The speed after $$ 20 $$ seconds is:
$$
v_f = v_i - a \cdot t = 200 \mathrm{~m/s} - (5 \mathrm{~m/s}^2 \cdot 20 \mathrm{s}) = 200 \mathrm{~m/s} - 100 \mathrm{~m/s} = 100 \mathrm{~m/s}
$$
To find the time to come to a stop:
$$
t = \frac{v_i}{a} = \frac{200 \mathrm{~m/s}}{5 \mathrm{~m/s}^2} = 40 \mathrm{s}
$$

### Summary of Results
1. Acceleration is the rate of change of velocity.
2. $$ a = 0 \mathrm{~m/s}^2 $$
3. $$ a \approx 0.0386 \mathrm{~m/s}^2 $$
4. $$ a = 0 \mathrm{~m/s}^2 $$
5. $$ a = 2.5 \mathrm{~m/s}^2 $$
6. Final speed $$ v_f = 38 \mathrm{~m/s} $$
7. $$ a = 0 \mathrm{~m/s}^2 $$
8. Time $$ t \approx 5 \mathrm{s} $$
9. $$ a = -7 \mathrm{~m/s}^2 $$
10. Speed after $$ 20 $$ seconds $$ v_f = 100 \mathrm{~m/s} $$, time to stop $$ t = 40 \mathrm{s} $$
1. Acceleration is the rate at which velocity changes. 2. A car moving at a constant speed of $$100 \mathrm{~km/h}$$ has an acceleration of $$0 \mathrm{~m/s}^2$$. 3. A car increasing its speed from rest to $$100 \mathrm{~km/h}$$ in $$0.2$$ hours has an acceleration of approximately $$0.0386 \mathrm{~m/s}^2$$. 4. Light traveling at a constant speed of $$300,000 \mathrm{~km/s}$$ has an acceleration of $$0 \mathrm{~m/s}^2$$. 5. A dragster accelerating from $$15 \mathrm{~m/s}$$ to $$25 \mathrm{~m/s}$$ in $$4$$ seconds has an acceleration of $$2.5 \mathrm{~m/s}^2$$. 6. A car accelerating from $$30 \mathrm{~m/s}$$ at $$2 \mathrm{~m/s}^2$$ for $$4$$ seconds reaches a final speed of $$38 \mathrm{~m/s}$$. 7. A cyclist pedaling at a constant speed of $$6 \mathrm{~m/s}$$ has an acceleration of $$0 \mathrm{~m/s}^2$$. 8. A Porsche accelerates from rest to $$125 \mathrm{~km/h}$$ in approximately $$5$$ seconds. 9. A car decelerating from $$35 \mathrm{~m/s}$$ to rest in $$5$$ seconds has an acceleration of $$-7 \mathrm{~m/s}^2$$. 10. A rocket decelerating at $$5 \mathrm{~m/s}^2$$ from an initial speed of $$200 \mathrm{~m/s}$$ reaches a speed of $$100 \mathrm{~m/s}$$ after $$20$$ seconds and comes to a stop in $$40$$ seconds.

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