A scooter company gives the following specifications about its product.
Weight of the scooter -95 kg
Maximum speed -60 km/h
Maximum engine power -3.5 hp
Pick up time to get the maximum speed -5s
Check the validity of these specifications.

Explanation

To check the validity of the scooter company's specifications, we will go through the following steps:

### Step 1: Convert Maximum Speed from km/h to m/s
The maximum speed given is 60 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]
Thus,
\[ 60 \text{ km/h} = 60 \times \frac{1}{3.6} \text{ m/s} = \frac{60}{3.6} \text{ m/s} = \frac{600}{36} \text{ m/s} = \frac{50}{3} \text{ m/s} \approx 16.67 \text{ m/s} \]

### Step 2: Calculate Maximum Acceleration
The scooter reaches its maximum speed in 5 seconds. We can calculate the maximum acceleration using the formula:
\[ \text{Acceleration} (a) = \frac{\text{Change in Velocity}}{\text{Time}} = \frac{v_f - v_i}{t} \]
Here, \(v_f = \frac{50}{3} \text{ m/s}\), \(v_i = 0 \text{ m/s}\), and \(t = 5 \text{ s}\):
\[ a = \frac{\frac{50}{3} - 0}{5} = \frac{50}{15} = \frac{10}{3} \text{ m/s}^2 \approx 3.33 \text{ m/s}^2 \]

### Step 3: Calculate Force Exerted by the Engine
Using Newton's second law, the force exerted by the engine can be calculated as:
\[ F = m \cdot a \]
Where \(m = 95 \text{ kg}\) and \(a = \frac{10}{3} \text{ m/s}^2\):
\[ F = 95 \cdot \frac{10}{3} = \frac{950}{3} \text{ N} \approx 316.67 \text{ N} \]

### Step 4: Convert Engine Power from hp to Watts
The maximum engine power is given as 3.5 hp. To convert this to watts, we use the conversion:
\[ 1 \text{ hp} = 746 \text{ W} \]
Thus,
\[ \text{Power} = 3.5 \times 746 \text{ W} = 2611 \text{ W} \]

### Step 5: Check the Validity of Specifications
To check if the specifications are valid, we will use the relationship between power, force, and velocity:
\[ \text{Power} = F \cdot v \]
Rearranging gives us:
\[ v = \frac{\text{Power}}{F} \]
Substituting the values we calculated:
\[ v = \frac{2611}{\frac{950}{3}} = \frac{2611 \cdot 3}{950} \approx 8.25 \text{ m/s} \]

### Step 6: Compare Maximum Speed with Calculated Speed
The calculated maximum speed from the power and force is approximately 8.25 m/s, while the specified maximum speed is \(\frac{50}{3} \approx 16.67 \text{ m/s}\). Since 8.25 m/s is significantly less than 16.67 m/s, the specifications provided by the scooter company are not valid.

### Conclusion
The specifications of the scooter regarding maximum speed are incorrect based on the calculations performed.

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