Question

A scooter company gives the following specifications about its product.
-Weight of scooter $95\,kg$.
-Maximum Speed $60\,kmh{r^{ - 1}}$.
-Maximum engine power $3.5\,hp$.
-Pick up time to get maximum speed $5\,s$.
Check the validity of these specifications.

Answer 1

Hint: In order to solve this question we need to understand what power of any device is. Power of a device is defined as a scalar product of force and velocity. It physically depicts how much energy any device can generate in a second. The more the energy is, the more efficient a device is. Also maximum speed means the largest distance a body covers in minimum time.

Complete step by step answer:
First we have to convert given values into SI units of each system.We know $1\,km = 1000\,m$ and $1hr = 3600\,\sec $.So Maximum speed of vehicle in SI unit is $60 \times \dfrac{{1000}}{{3600}}\,m\,{\sec ^{ - 1}}$ which is $16.67\,m\,{\sec ^{ - 1}}$.So the maximum speed of a vehicle is $16.67\,m\,{\sec ^{ - 1}}$.
So the maximum energy it can generate is given by,
$E = \dfrac{1}{2}m{v^2}$
Where “m” is mass of body and “v” is speed.
Since $m = 95kg$ given in question and $v = 16.67\,m\,{\sec ^{ - 1}}$

So putting values we get
$E = \dfrac{1}{2}(95 \times 16.67 \times 16.67)$
$E = 13194.45J$
So the power of engine it can generate is $P = \dfrac{E}{t}$
Where “E” is energy and “t” is time.
$t = 5{\sec ^{ - 1}}$
Given in question and $E = 13194.15J$
Putting values we get
$P = \dfrac{{13194.45}}{5}\,J{\sec ^{ - 1}}$
$\Rightarrow P = 2638.89\,J{\sec ^{ - 1}}$
Using conversion of $1J{\sec ^{ - 1}} = 0.0013\,hp$
$P = (2638.89 \times 0.0013)hp$
$\therefore P = 3.43\,hp$

Hence, given Specification is correct to near value and there is not much error.

Note:It should be remembered that horse power is the standard unit for denoting power of a vehicle. The more efficient the vehicle is, the more the engine horsepower. Also weight of any device is defined as a product of matter mass and acceleration due to gravity.Also Power is defined as Energy per unit time and product of force into velocity.