A loaded truck can accelerate at 4.8 m/s2. It loses its load so that it is only 0.4 as massive.
By what factor must the acceleration change for the same driving force?
To answer this question, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma). Let's denote the mass of the loaded truck as m and the acceleration as a.
Given that the loaded truck can accelerate at 4.8 m/s^2, we can write the equation as:
F = m * a
Now, let's consider the situation after the truck loses its load. The new mass of the truck is 0.4 times the original mass, which can be written as 0.4m. We need to find the new acceleration, which we can denote as a'.
According to Newton's second law of motion, the force acting on the truck after losing its load is the same as before because the driving force remains constant. Therefore, we can write:
F = m * a = (0.4m) * a'
We can now solve for a' by rearranging the equation:
a' = (m * a) / (0.4m)
Simplifying the equation, we find:
a' = (a) / (0.4)
To find the factor by which the acceleration must change, we can simply divide the new acceleration by the original acceleration:
Factor = a' / a = (a / 0.4) / a = 1 / 0.4 = 2.5
Therefore, the acceleration must change by a factor of 2.5 (or 2.5 times) for the same driving force.