“No Endurance Ned” accelerates from rest at a rate of 6 m/s 2 for the first 20 meters and then runs at a constant velocity for the final 20 meters. 

Let's break down the problem involving "No Endurance Ned" into two phases:

1. **Phase 1**: Ned accelerates from rest at a rate of \( a = 6 \, \text{m/s}^2 \) for the first 20 meters.
2. **Phase 2**: After reaching 20 meters, Ned runs at a constant velocity for the final 20 meters.

### Phase 1: Accelerating from rest

We use the equation of motion for uniformly accelerated motion:
\[
v^2 = u^2 + 2as
\]
Where:
- \( u = 0 \, \text{m/s} \) (since he starts from rest),
- \( a = 6 \, \text{m/s}^2 \) (given acceleration),
- \( s = 20 \, \text{m} \) (distance for the first phase).

Substituting values:
\[
v^2 = 0 + 2(6)(20) = 240
\]
\[
v = \sqrt{240} \approx 15.49 \, \text{m/s}
\]
So, Ned reaches a velocity of approximately \( 15.49 \, \text{m/s} \) at the end of the first 20 meters.

Now, to find the time it takes for the first phase, we use the equation:
\[
v = u + at
\]
Substituting the known values:
\[
15.49 = 0 + 6t
\]
\[
t = \frac{15.49}{6} \approx 2.58 \, \text{seconds}
\]
So, it takes about \( 2.58 \, \text{seconds} \) for Ned to cover the first 20 meters.

### Phase 2: Constant velocity

In this phase, Ned runs at the constant velocity he reached at the end of Phase 1, which is \( v = 15.49 \, \text{m/s} \). 

The time to cover the final 20 meters is:
\[
t = \frac{\text{distance}}{\text{velocity}} = \frac{20}{15.49} \approx 1.29 \, \text{seconds}
\]

### Total time for the race
The total time Ned takes to complete the entire 40 meters is the sum of the time for both phases:
\[
t_{\text{total}} = 2.58 \, \text{seconds} + 1.29 \, \text{seconds} \approx 3.87 \, \text{seconds}
\]

Thus, Ned takes approximately **3.87 seconds** to complete the 40 meters.

---

Would you like more details or explanations on any part of the process?

### Related Questions:
1. What would happen if Ned's acceleration were doubled?
2. How much distance would Ned cover if he accelerated for 30 meters instead?
3. How would the total time change if the final distance were 40 meters at constant speed?
4. Can we determine the average velocity of Ned during the entire run?
5. How would air resistance affect Ned's time in reality?

#### Tip:
Always check units when solving physics problems. It helps avoid mistakes and ensures consistency in calculations.

“No Endurance Ned” accelerates from rest at a rate of 6 m/s² for the first 20 meters and then runs at a constant velocity for the final 20 meters.

Solve the kinematics problem where 'No Endurance Ned' accelerates at 6 m/s² for 20 meters and runs at constant velocity for the next 20 meters. Learn how to apply equations of motion and calculate total time. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation