Acceleration Worksheet (WITH ANSWERS) - Free Printable

Let's solve each of these acceleration and time-related problems step by step, starting with the foundational equation.

---

1. Write down the acceleration equation.

The acceleration equation is:

\[
a = \frac{v - u}{t}
\]

Where:
- \( a \) = acceleration (in m/s²)
- \( v \) = final velocity (in m/s)
- \( u \) = initial velocity (in m/s)
- \( t \) = time taken (in seconds)

---

2. A man running at 5 m/s increases his velocity to 10 m/s in 2 seconds. What is his acceleration?

Given:
- \( u = 5 \, \text{m/s} \)
- \( v = 10 \, \text{m/s} \)
- \( t = 2 \, \text{s} \)

Using the formula:

\[
a = \frac{v - u}{t} = \frac{10 - 5}{2} = \frac{5}{2} = 2.5 \, \text{m/s}^2
\]

✔ Answer: 2.5 m/s²

---

3. A car accelerates from rest to a speed of 50 m/s in 4 seconds. What was its acceleration?

"From rest" means initial velocity \( u = 0 \, \text{m/s} \)

Given:
- \( u = 0 \, \text{m/s} \)
- \( v = 50 \, \text{m/s} \)
- \( t = 4 \, \text{s} \)

\[
a = \frac{50 - 0}{4} = \frac{50}{4} = 12.5 \, \text{m/s}^2
\]

✔ Answer: 12.5 m/s²

---

4. A train travelling at 100 m/s slows down and stops at a platform in 25 seconds. What was its acceleration?

"Slows down and stops" → final velocity \( v = 0 \, \text{m/s} \)

Given:
- \( u = 100 \, \text{m/s} \)
- \( v = 0 \, \text{m/s} \)
- \( t = 25 \, \text{s} \)

\[
a = \frac{0 - 100}{25} = \frac{-100}{25} = -4 \, \text{m/s}^2
\]

Negative sign indicates deceleration (slowing down).

✔ Answer: -4 m/s² (or deceleration of 4 m/s²)

---

5. Extension: A car travels from 0 to 20 km/h in 0.5 seconds. What is its acceleration in m/s²?

First, convert 20 km/h to m/s:

\[
20 \, \text{km/h} = \frac{20 \times 1000}{3600} = \frac{20000}{3600} \approx 5.56 \, \text{m/s}
\]

Now:
- \( u = 0 \, \text{m/s} \)
- \( v = 5.56 \, \text{m/s} \)
- \( t = 0.5 \, \text{s} \)

\[
a = \frac{5.56 - 0}{0.5} = \frac{5.56}{0.5} = 11.12 \, \text{m/s}^2
\]

✔ Answer: Approximately 11.12 m/s²

---

6. Write down the acceleration equation, rearranged for time.

Starting from:

\[
a = \frac{v - u}{t}
\]

Multiply both sides by \( t \):

\[
a \cdot t = v - u
\]

Divide both sides by \( a \):

\[
t = \frac{v - u}{a}
\]

✔ Rearranged equation: \( t = \frac{v - u}{a} \)

---

7. A rocket is flying at 400 m/s and accelerates at 20 m/s² until it reaches its top speed of 1000 m/s. How much time does this take?

Given:
- \( u = 400 \, \text{m/s} \)
- \( v = 1000 \, \text{m/s} \)
- \( a = 20 \, \text{m/s}^2 \)

Use the rearranged time formula:

\[
t = \frac{v - u}{a} = \frac{1000 - 400}{20} = \frac{600}{20} = 30 \, \text{seconds}
\]

✔ Answer: 30 seconds

---

✔ Final Answers Summary:

1. \( a = \frac{v - u}{t} \)
2. \( 2.5 \, \text{m/s}^2 \)
3. \( 12.5 \, \text{m/s}^2 \)
4. \( -4 \, \text{m/s}^2 \)
5. \( 11.12 \, \text{m/s}^2 \)
6. \( t = \frac{v - u}{a} \)
7. \( 30 \, \text{seconds} \)

Let me know if you'd like a diagram or further explanation!