an unloaded van has a acceleration of 5 m/s/s. a fully loaded van weighs twice as much as the unloaded van. what is the acceleration of the fully loaded van if the forward thrust remains the same?
F = m a
double m, half a
To determine the acceleration of the fully loaded van, let's break down the problem step by step.
1. Start by considering the unloaded van. The given information is that it has an acceleration of 5 m/s². Let's call the mass of the unloaded van "m."
2. According to Newton's second law of motion, force (F) is equal to mass (m) multiplied by acceleration (a).
F = m * a
3. Now, let's consider the fully loaded van. The question states that the loaded van weighs twice as much as the unloaded van. Therefore, the mass of the loaded van would be twice the mass of the unloaded van, i.e., 2m.
4. The forward thrust remains the same for both vans. This means that the force acting on the unloaded van is the same as the force acting on the loaded van.
5. Since force is equal to mass multiplied by acceleration, we can equate the forces acting on both vans:
F(unloaded van) = F(loaded van)
Considering the expressions for force in terms of mass and acceleration:
m * a(unloaded van) = (2m) * a(loaded van)
6. Simplifying the equation by canceling out the mass factor:
a(unloaded van) = 2 * a(loaded van)
7. Rearranging the equation to solve for the acceleration of the loaded van:
a(loaded van) = a(unloaded van) / 2
8. Substituting the value of the unloaded van's acceleration:
a(loaded van) = 5 m/s² / 2
9. Calculating the result:
a(loaded van) = 2.5 m/s²
Therefore, the acceleration of the fully loaded van, given that the forward thrust remains the same, is 2.5 m/s².