Acceleration Problems: 1. Acceleration is the rate at which what changes? 2. What is the acceleration of a car moving in a straight-line path that travels at constant speed of $$ 100 \mathrm{~km} / \mathrm{h} $$ ? 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 ? 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? 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? 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? 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? 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? 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? 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?

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UpStudy AI · Accepted Answer

Sure, let's tackle each of these acceleration problems one by one.

---

### **1. Acceleration is the rate at which what changes?**

**Answer:**  
**Acceleration** is the rate at which **velocity** changes over time. It quantifies how quickly an object is speeding up, slowing down, or changing direction.

---

### **2. What is the acceleration of a car moving in a straight-line path that travels at a constant speed of $$ 100 \, \mathrm{km/h} $$?**

**Answer:**  
If a car is moving at a **constant speed**, its velocity is not changing. Therefore, the **acceleration is zero**.

$$
\boxed{0 \, \mathrm{m/s}^2}
$$

---

### **3. What is the acceleration of a car moving in a straight-line path that increases its speed from rest to $$ 100 \, \mathrm{km/h} $$ in 0.2 hours?**

**Solution:**  
First, convert all units to SI units for consistency.

- **Initial velocity ($$ u $$)**: 0 (starting from rest)
- **Final velocity ($$ v $$)**: $$ 100 \, \mathrm{km/h} = \frac{100 \times 1000}{3600} \, \mathrm{m/s} \approx 27.78 \, \mathrm{m/s} $$
- **Time ($$ t $$)**: 0.2 hours = $$ 0.2 \times 3600 \, \mathrm{s} = 720 \, \mathrm{s} $$

**Acceleration ($$ a $$)** is given by:

$$
a = \frac{v - u}{t} = \frac{27.78 \, \mathrm{m/s} - 0}{720 \, \mathrm{s}} \approx 0.0386 \, \mathrm{m/s}^2
$$

**Answer:**  
$$
\boxed{0.0386 \, \mathrm{m/s}^2}
$$

---

### **4. Light travels in a straight line at a constant speed of $$ 300,000 \, \mathrm{km/s} $$. What would the acceleration of light 3 seconds later be?**

**Answer:**  
Since light travels at a **constant speed**, its velocity does not change over time. Therefore, the **acceleration is zero**.

$$
\boxed{0 \, \mathrm{m/s}^2}
$$

---

### **5. A dragster going at $$ 15 \, \mathrm{m/s} $$ north increases its velocity to $$ 25 \, \mathrm{m/s} $$ north in 4 seconds. What's its acceleration during that time interval?**

**Solution:**  
$$
a = \frac{\Delta v}{t} = \frac{25 \, \mathrm{m/s} - 15 \, \mathrm{m/s}}{4 \, \mathrm{s}} = \frac{10 \, \mathrm{m/s}}{4 \, \mathrm{s}} = 2.5 \, \mathrm{m/s}^2
$$

**Answer:**  
$$
\boxed{2.5 \, \mathrm{m/s}^2 \text{ north}}
$$

---

### **6. A car going $$ 30 \, \mathrm{m/s} $$ undergoes an acceleration of $$ 2 \, \mathrm{m/s}^2 $$ for 4 seconds. What is its final speed?**

**Solution:**  
$$
v = u + a \times t = 30 \, \mathrm{m/s} + (2 \, \mathrm{m/s}^2 \times 4 \, \mathrm{s}) = 30 \, \mathrm{m/s} + 8 \, \mathrm{m/s} = 38 \, \mathrm{m/s}
$$

**Answer:**  
$$
\boxed{38 \, \mathrm{m/s}}
$$

---

### **7. A man on a unicycle pedals for 2 seconds at a speed of $$ 6 \, \mathrm{m/s} $$ and then pedals another 2 seconds at a rate of $$ 6 \, \mathrm{m/s} $$. What is the acceleration of the cyclist?**

**Answer:**  
Since the cyclist maintains a **constant speed** of $$ 6 \, \mathrm{m/s} $$ throughout, there is **no change in velocity**. Therefore, the **acceleration is zero**.

$$
\boxed{0 \, \mathrm{m/s}^2}
$$

---

### **8. If a Porsche accelerates at a rate of $$ 25 \, \mathrm{km/h \cdot s} $$ and goes from rest to $$ 125 \, \mathrm{km/h} $$. How long did it take the car to reach its final speed?**

**Solution:**  
$$
a = 25 \, \mathrm{km/h \cdot s}, \quad v = 125 \, \mathrm{km/h}, \quad u = 0 \, \mathrm{km/h}
$$

$$
t = \frac{v - u}{a} = \frac{125 \, \mathrm{km/h} - 0}{25 \, \mathrm{km/h \cdot s}} = 5 \, \mathrm{seconds}
$$

**Answer:**  
$$
\boxed{5 \, \mathrm{seconds}}
$$

---

### **9. If a car is traveling at $$ 35 \, \mathrm{m/s} $$ and the driver sees a deer and slams on her brakes to come to a stop in 5 seconds, what is her rate of acceleration?**

**Solution:**  
$$
a = \frac{\Delta v}{t} = \frac{0 \, \mathrm{m/s} - 35 \, \mathrm{m/s}}{5 \, \mathrm{s}} = \frac{-35 \, \mathrm{m/s}}{5 \, \mathrm{s}} = -7 \, \mathrm{m/s}^2
$$

The negative sign indicates **deceleration**.

**Answer:**  
$$
\boxed{-7 \, \mathrm{m/s}^2}
$$

---

### **10. A rocket decelerates at a rate of $$ 5 \, \mathrm{m/s}^2 $$. If the initial velocity of the rocket was $$ 200 \, \mathrm{m/s} $$, how fast would the rocket be traveling 20 seconds later? How long will it take before the rocket comes to a stop?**

**Solution:**

**a. Velocity after 20 seconds:**
$$
v = u + a \times t = 200 \, \mathrm{m/s} + (-5 \, \mathrm{m/s}^2 \times 20 \, \mathrm{s}) = 200 \, \mathrm{m/s} - 100 \, \mathrm{m/s} = 100 \, \mathrm{m/s}
$$

**b. Time to come to a stop:**
$$
0 = 200 \, \mathrm{m/s} + (-5 \, \mathrm{m/s}^2) \times t \
t = \frac{-200 \, \mathrm{m/s}}{-5 \, \mathrm{m/s}^2} = 40 \, \mathrm{seconds}
$$

**Answer:**  
- After **20 seconds**, the rocket is traveling at:
  $$
  \boxed{100 \, \mathrm{m/s}}
  $$
- It will take **40 seconds** for the rocket to come to a complete stop:
  $$
  \boxed{40 \, \mathrm{seconds}}
  $$

---

If you have any further questions or need additional explanations, feel free to ask!
1. **Acceleration is the rate at which velocity changes.** 2. **The car's acceleration is 0 m/s².** 3. **The car's acceleration is 0.0386 m/s².** 4. **Light's acceleration is 0 m/s².** 5. **The dragster's acceleration is 2.5 m/s² north.** 6. **The car's final speed is 38 m/s.** 7. **The cyclist's acceleration is 0 m/s².** 8. **It took 5 seconds for the Porsche to reach 125 km/h.** 9. **The car's acceleration is -7 m/s².** 10. **After 20 seconds, the rocket is traveling at 100 m/s. It will take 40 seconds to stop.**

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