Question

Let’s assume that the car of mass 1550 kg, can reach a speed of 26.8 m/s in 7.1 s. What is the average power needed to accomplish this? (Given: 1 hp=746 Watt)
A. 105 hp
B. 110 hp
C. 1210 hp
D. 1040 hp

Answer 1

Hint:This problem can be solved by using the definition of the quantity power. The power is derived from another quantity called work. Their relationship is given by –
Power is the rate of work done per unit time.
Power, $P = \dfrac{W}{t}$
where W = work, t = time.

Complete step by step solution:
The work done is the product of force and the displacement caused by the body.
$W = F \times s$
The kinetic energy is the energy associated with an object by the virtue of its motion. It is given by the formula –
$KE = \dfrac{1}{2}m{v^2}$
where m is the mass of the body and v is the velocity of the body.
The work-energy theorem gives the correlation between work and energy. It states that the work done by an object is equal to the loss of energy in the body, which is translated as the kinetic energy in the body.
Thus,
$W = KE$
Power is the defined as the amount of energy or the work done per unit time.
Power, $P = \dfrac{W}{t}$
where W = work, t = time.
By work-energy theorem, we get –
$P = \dfrac{{KE}}{t}$

Given,
Mass of the car, $m = 1550kg$
Velocity of the car, $v = 26 \cdot 8m{s^{ - 1}}$
Time taken, $t = 7 \cdot 1s$
The kinetic energy
$KE = \dfrac{1}{2}m{v^2} = \dfrac{1}{2} \times 1550 \times 26 \cdot {8^2} = 556636J$
Power,
$P = \dfrac{{KE}}{t} = \dfrac{{556636}}{{7 \cdot 1}} = 78399 \cdot 436W$
Here, we have obtained the power in the SI unit i.e. watt (W). However, there is another unit called horsepower.
One horsepower is defined as the work done by a horse in lifting 75 kilograms of mass by 1 metre in 1 second.
The relation to the SI unit is given by:
1 horsepower (hp) = 746 watts (W)
Thus, converting the power obtained to horsepower, we get –
$P = \dfrac{{78399 \cdot 43}}{{746}} = 105$ hp

Hence, the correct answer is Option A.

Note:Even though the SI unit of power is watt, it is widely used in the electric industry and for mechanical industry such as engines of automobiles, the widely used unit worldwide, is horsepower. More commonly, the power of an automobile engine is denoted in terms of a unit Brake Horsepower or BHP.