The mass of the first car m1 is greater than the mass of the second car m2 by m = 5 t.

The mass of the first car m1 is greater than the mass of the second car m2 by m = 5 t. What are the masses of the cars if, under the action of the same forces, they acquire accelerations a1 = 1 m / s and a2 = 1.1 m / s? Friction is neglected.

In accordance with Newton’s second law, the acceleration a acquired by a body is directly proportional to the force F causing it and inversely proportional to the body’s mass m. For two cars we have:
a1 = F1 / m1;
a2 = F2 / m2.
By condition F1 = F2 = F, m2 = m1 – Δm. Then we get:
a1 = F / m1;
a2 = F / (m1 – Δm).
Let’s divide the first equation by the second:
a1 / a2 = [F / m1] / [F / (m1 – Δm)];
a1 / a2 = (m1 – Δm) / m1;
a1 / a2 = 1 – Δm / m1.
Let us express the mass of the first car m1:
m1 = Δm / (1 – a1 / a2);
m1 = 5 / (1 – 1 / 1.1) = 55 t.
Then the mass of the second car is
m2 = m1 – Δm;
m2 = 55 – 5 = 50 t.