Solve the problem.
-If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 16 kilograms accelerates at a rate of 10 meters per second per second by a force,
Find the rate of acceleration of an object with a mass of 4 kilograms that is pulled by the same force.

Question

Quizplus · Accepted Answer

According to the problem, acceleration is inversely proportional to mass. So, we can use the formula:
a1/m1 = a2/m2
where a1 = 10 m/s^2, m1 = 16 kg, and a2 is the acceleration we need to find for a mass of 4 kg.
Plugging in the values, we get:
10/16 = a2/4
Solving for a2, we get:
a2 = (10/16) * 4 = 2.5 m/s^2
Therefore, the rate of acceleration for the 4 kg object pulled by the same force is 2.5 m/s^2, which corresponds to choice B. Since the force acting on the object stays the same, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration. From the given information, we know that F = 16 x 10 = 160 N (newtons). Since the acceleration is inversely proportional to the mass, we have the equation a1/a2 = m2/m1, where a1 is the acceleration of the 16 kg object, a2 is the acceleration of the 4 kg object, m1 is the mass of the 16 kg object, and m2 is the mass of the 4 kg object. Substituting in the values we know, we get 10/a2 = 4/16, which simplifies to a2 = 40 m/s^2. Therefore, the rate of acceleration of the object with a mass of 4 kg is 40 m/s^2, which corresponds to choice B.

Solve the Problem. -If the Force Acting on an Object Stays the Same