Answer to Question #99601 in Quantum Mechanics for Pakeeza Mazhar

Question

the cars begin to move with the green light having mass 2m and same direction with accerlation of a/2

Answer 1

We can compare two cars that simultaneously started racing: one with mass 2m and acceleration a/2 and the other with mass m and acceleration a. We can calculate what force their engines have developed according to Newton's second law:

$$F_1=2m\cdot a/2=ma,\\ F_2=ma.$$

We see that the force is the same. Indeed, since the first car's mass is two times larger than the other's, the acceleration at the same force will be two times less.

But let us calculate the speed the cars will reach at the next traffic light in d meters away:

$$v_1=\sqrt{2\cdot \frac{a}{2}\cdot d}=\sqrt{ad},\\ v_2=\sqrt{2ad}=1.4\sqrt{ad}.$$

Thus, we see that the car with mass m achieves the speed just 1.4 times (not 2) more that the car with mass 2m with the same engine.