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Question
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 − 5 s
Check the validity of these specifications.
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Solution
The specifications given by the company are:
\[\text{ Mass, m = 95 kg } \]
\[\text{ Maximum power, P_m = 3 . 5 hp } \]
\[\text{ Maximum speed, v}_\text{m }= 60 \text{ km /h} \]
\[ = \frac{50}{3} \text{ m/s } \]
\[\text{ Pick up time to get maximum speed, t}_\text{m }= 5 \sec\]
So, the maximum acceleration that can be produced,
\[\text{ a }= \frac{50}{3 \times 5} = \frac{10}{3} \text{ m/ s} ^2\]
So, the driving force,
\[\text{ F = ma } = 95 \times \left( \frac{10}{3} \right)\]
\[ = \frac{950}{3} \text{ N } \]
\[\text{ Max speed, } \nu = \frac{\text{ p } }{\text{ F } }\]
\[ \Rightarrow \text{ v }=3.5\times746\times\frac{3}{950}\Rightarrow8.2 \text{ m/s } \]
As the scooter can reach a maximum of 8.2 m/s while producing a force of 950/3 N, the specifications given are not correct.
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