Find mass when knowing distance

Question

A toy truck from starting position within a certain time moved 60 cm. After adding 200 g mass weight onto the truck, the truck during the same amount of time moved 20 cm. Find the mass of the toy truck. Answer is 100 g

Answer 1

It sounds as though the same net force must be applied in both cases, first to the truck alone and then to the truck with the additional 200 gram mass. If that is the case, then we can apply Newton's second law along with a kinematics equation to answer this question.

Newton's second law (net force = m*a) tells us that, if the same force is applied in both instances, then the product of mass times acceleration must be the same for both cases as well:

F₁ = F₂ means that m₁a₁ = m₂a₂

Using the kinematics formula d = 1/2 a t², we can find the ratio of accelerations. Since the time is identical for both trials, we see that distance traveled is directly proportional to acceleration. The unloaded truck traveled three times as far as the loaded one, so it must have three times the acceleration.

Going back to our work with the second law, we see that, if the unloaded truck has three times the acceleration, then the loaded truck has three times the mass: m(3a) = (3m)(a).

Let the symbol "M" stand for the mass of the truck alone. Then we see that M + 200 = 3M. Then 2M = 200 and M = 100 grams.