A powerful motorcycle can accelerate from rest to 26 m/s in only 3.2s. How far does it travel in that time? (Express the numeral of your answer in SI units)

To solve the problem, we can use the kinematic equation for uniformly accelerated motion:

\[
s = ut + \frac{1}{2}at^2
\]

Where:
- \( s \) is the distance traveled.
- \( u \) is the initial velocity (which is 0 m/s since the motorcycle starts from rest).
- \( t \) is the time taken, which is 3.2 seconds.
- \( a \) is the acceleration.

First, we need to calculate the acceleration using the following formula:

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

Where:
- \( v \) is the final velocity, which is 26 m/s.
- \( u \) is the initial velocity, which is 0 m/s.
- \( t \) is the time, which is 3.2 seconds.

Now, let's calculate the acceleration:

\[
a = \frac{26 \, \text{m/s} - 0 \, \text{m/s}}{3.2 \, \text{s}} = \frac{26 \, \text{m/s}}{3.2 \, \text{s}} = 8.125 \, \text{m/s}^2
\]

Now that we have the acceleration, we can calculate the distance traveled:

\[
s = 0 \times 3.2 \, \text{s} + \frac{1}{2} \times 8.125 \, \text{m/s}^2 \times (3.2 \, \text{s})^2
\]

\[
s = \frac{1}{2} \times 8.125 \, \text{m/s}^2 \times 10.24 \, \text{s}^2
\]

\[
s = 4.0625 \, \text{m/s}^2 \times 10.24 \, \text{s}^2 = 41.6 \, \text{m}
\]

So, the motorcycle travels **41.6 meters** in 3.2 seconds.

Would you like further details or have any questions?

---

Here are 5 related questions to consider:
1. What would be the distance traveled if the motorcycle took 4 seconds to reach 26 m/s?
2. How much time would it take for the motorcycle to travel 100 meters at this acceleration?
3. What is the motorcycle's speed after 2 seconds?
4. How would the distance change if the acceleration were doubled?
5. What would be the distance traveled if the initial velocity were 10 m/s instead of 0 m/s?

**Tip:** Always ensure that all units are consistent when solving kinematic equations.

Explore how a powerful motorcycle accelerates from rest to 26 m/s in 3.2 seconds and calculate the distance traveled using kinematic equations. Understand the concepts of uniformly accelerated motion and apply the formula s = ut + \frac{1}{2}at^2. Suitable for high school students studying physics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation