Question

The mass of Tesla Model S is 2000 kg and its engine produces

Answer 1

Answer:

The ratio of the power generated by the engines are $\dfrac{2}{3}$

(b) is correct option.

Explanation:

Given that,

Mass of Tesla = 2000 Kg

Torque = 400 Nm

Mass of Mercedes = 1.5 M Tesla

The Benz engine produces 50% more torque than the Tesla.

We need to calculate the power generated by the engines 6 seconds after a start from rest

Using formula of  power

$P=F\cdot v$

We know that,

$v=at$

$v=\dfrac{F}{m}t$

$v=\dfrac{\tau}{mr}t$

Put the value of F and v in equation (I)

$P=\dfrac{\tau}{r}\times\dfrac{\tau}{mr}t$

$P=\dfrac{\tau^2t}{mr^2}$

Here, r and t are same for both bodies.

$P\propto\dfrac{\tau^2}{m}$

We need to calculate the ratio of the power generated by the engines

Using formula of power

$\dfrac{P_{T}}{P_{B}}=\dfrac{\tau_{T}^2}{m_{T}}\times\dfrac{m_{B}}{\tau_{B}}$

Put the value into the formula

$\dfrac{P_{T}}{P_{B}}=\dfrac{400^2}{2000}\times\dfrac{3000}{600^2}$

$\dfrac{P_{T}}{P_{B}}=\dfrac{2}{3}$

Hence, The ratio of the power generated by the engines are $\dfrac{2}{3}$