2. Acyclist accelerates from 0m/s to 8m/s In 3 seconds. What is his acceleration? Is this acceleration higher than that of a car which accelerates from o to 27m/s in 8 seconds?

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2. Acyclist accelerates from 0m/s to 8m/s In 3 seconds. What is his acceleration? Is this acceleration higher than that of a car which accelerates from o to 27m/s in 8 seconds?

Answer 1

### The cyclist's acceleration is $\frac{8}{3} \, \text{m/s}^2$ and the car's acceleration is $\frac{27}{8} \, \text{m/s}^2$. The car's acceleration is higher.

Answer 2

## Step 1: Calculate the acceleration of the cyclist ### Use the formula for acceleration: $a = \frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time. For the cyclist, $\Delta v = 8 \, \text{m/s} - 0 \, \text{m/s} = 8 \, \text{m/s}$ and $\Delta t = 3 \, \text{s}$. Thus, $a_{\text{cyclist}} = \frac{8 \, \text{m/s}}{3 \, \text{s}} = \frac{8}{3} \, \text{m/s}^2$. ## Step 2: Calculate the acceleration of the car ### Similarly, for the car, $\Delta v = 27 \, \text{m/s} - 0 \, \text{m/s} = 27 \, \text{m/s}$ and $\Delta t = 8 \, \text{s}$. Thus, $a_{\text{car}} = \frac{27 \, \text{m/s}}{8 \, \text{s}} = \frac{27}{8} \, \text{m/s}^2$. ## Step 3: Compare the accelerations ### Compare the two accelerations: $\frac{8}{3} \, \text{m/s}^2$ and $\frac{27}{8} \, \text{m/s}^2$. Simplify the fractions to compare: $\frac{8}{3} \approx 2.67 \, \text{m/s}^2$ and $\frac{27}{8} \approx 3.375 \, \text{m/s}^2$. The car's acceleration is higher.

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2. Acyclist accelerates from 0m/s to 8m/s In 3 seconds. What is his acceleration? Is this acceleration higher than that of a car which accelerates from o to 27m/s in 8 seconds?

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