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



To calculate the acceleration, we use the formula:

\[
\text{acceleration} = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}}
\]

For the cyclist:
- Final velocity, \(v_f = 8 \, \text{m/s}\)
- Initial velocity, \(v_i = 0 \, \text{m/s}\) (since starting from rest)
- Time, \(t = 3 \, \text{seconds}\)

\[
a_{\text{cyclist}} = \frac{8 \, \text{m/s} - 0 \, \text{m/s}}{3 \, \text{seconds}} = \frac{8}{3} \, \text{m/s}^2 \approx 2.67 \, \text{m/s}^2
\]

Now for the car:
- Final velocity, \(v_f = 30 \, \text{m/s}\)
- Initial velocity, \(v_i = 0 \, \text{m/s}\)
- Time, \(t = 8 \, \text{seconds}\)

\[
a_{\text{car}} = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{8 \, \text{seconds}} = \frac{30}{8} \, \text{m/s}^2 = 3.75 \, \text{m/s}^2
\]

### Conclusion:
- Cyclist's acceleration: \(2.67 \, \text{m/s}^2\)
- Car's acceleration: \(3.75 \, \text{m/s}^2\)

The car has a higher acceleration than the cyclist.

Would you like more details or have any questions?

### Related questions:
1. What would the velocity of the cyclist be after 5 seconds, assuming constant acceleration?
2. How far did the cyclist travel in those 3 seconds of acceleration?
3. If the cyclist continued at 8 m/s, how far would they travel in the next 5 seconds?
4. What is the definition of uniform acceleration?
5. How does acceleration relate to force according to Newton's Second Law?

### Tip:
Remember that acceleration is directly proportional to the change in velocity over time.

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

Determine the acceleration of a cyclist and compare it to that of a car. This problem involves calculating acceleration using the formula (Final velocity - Initial velocity) / Time, suitable for Grade 8 students learning basic kinematics concepts.

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