Acceleration Worksheet featuring equations and five problems related to calculating average acceleration, final velocity, and time using the GUESS method.

Let's solve each problem using the GUESS method, which stands for:

- Given
- Unknown
- Equation
- Substitute
- Solve

We’ll apply this to each problem step by step.

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Problem 1:

A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration?

#### G: Given
- Initial velocity ($v_i$) = 4 m/s
- Final velocity ($v_f$) = 22 m/s
- Time ($t$) = 3 s

#### U: Unknown
- Acceleration ($a$) = ?

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

#### S: Substitute
$$
a = \frac{22\, \text{m/s} - 4\, \text{m/s}}{3\, \text{s}} = \frac{18\, \text{m/s}}{3\, \text{s}}
$$

#### S: Solve
$$
a = 6\, \text{m/s}^2
$$

✔ Answer: The average acceleration is 6 m/s².

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Problem 2:

A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration? Is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds?

#### Part A: Cyclist’s acceleration

#### G:
- $v_i = 0$ m/s
- $v_f = 8$ m/s
- $t = 3$ s

#### U:
- $a = ?$

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

#### S:
$$
a = \frac{8 - 0}{3} = \frac{8}{3} \approx 2.67\, \text{m/s}^2
$$

#### S:
Cyclist’s acceleration = 2.67 m/s²

---

#### Part B: Car’s acceleration

#### G:
- $v_i = 0$ m/s
- $v_f = 30$ m/s
- $t = 8$ s

#### U:
- $a = ?$

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

#### S:
$$
a = \frac{30 - 0}{8} = \frac{30}{8} = 3.75\, \text{m/s}^2
$$

#### S:
Car’s acceleration = 3.75 m/s²

Now compare:
- Cyclist: 2.67 m/s²
- Car: 3.75 m/s²

So, no, the cyclist’s acceleration is not higher than the car’s.

✔ Answer:
- Cyclist’s acceleration = 2.67 m/s²
- Car’s acceleration = 3.75 m/s²
- No, the cyclist’s acceleration is not higher.

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Problem 3:

A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Find the car’s average acceleration.

#### G:
- $v_i = 0$ (rest)
- $v_f = 70$ km/h
- $t = 7$ s

But units must match! Convert km/h to m/s.

$$
70\, \text{km/h} = \frac{70 \times 1000}{3600} = \frac{70000}{3600} \approx 19.44\, \text{m/s}
$$

So:
- $v_f = 19.44$ m/s
- $t = 7$ s

#### U:
- $a = ?$

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

#### S:
$$
a = \frac{19.44 - 0}{7} = \frac{19.44}{7} \approx 2.78\, \text{m/s}^2
$$

#### S:
$$
a \approx 2.78\, \text{m/s}^2
$$

✔ Answer: The car’s average acceleration is approximately 2.78 m/s².

---

Problem 4:

A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard’s average acceleration?

#### G:
- $v_i = 2$ m/s
- $v_f = 10$ m/s
- $t = 4$ s

#### U:
- $a = ?$

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

#### S:
$$
a = \frac{10 - 2}{4} = \frac{8}{4} = 2\, \text{m/s}^2
$$

#### S:
$$
a = 2\, \text{m/s}^2
$$

✔ Answer: The lizard’s average acceleration is 2 m/s².

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Problem 5:

If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s² for 3 seconds, what will its final velocity be?

Wait — accelerates at a rate of 50 m/s²? That seems extremely high (typical cars are around 1–10 m/s²). But let's assume it's correct.

#### G:
- $v_i = 10$ m/s
- $a = 50$ m/s²
- $t = 3$ s

#### U:
- $v_f = ?$

#### E:
$$
v_f = a \cdot t + v_i
$$

#### S:
$$
v_f = (50\, \text{m/s}^2)(3\, \text{s}) + 10\, \text{m/s} = 150 + 10 = 160\, \text{m/s}
$$

#### S:
$$
v_f = 160\, \text{m/s}
$$

✔ Answer: The final velocity is 160 m/s.

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✔ Final Answers Summary:

1. Roller coaster: $6\, \text{m/s}^2$
2. Cyclist: $2.67\, \text{m/s}^2$, No, not higher than car ($3.75\, \text{m/s}^2$)
3. Car: $2.78\, \text{m/s}^2$
4. Lizard: $2\, \text{m/s}^2$
5. Ferrari: $160\, \text{m/s}$

All problems solved using GUESS method as required. Let me know if you'd like these formatted neatly for printing or submission!