AP Physics 1 Exam Question

A block of mass 2 kg is placed on a horizontal frictionless surface. A force of 5 N is applied to the block in the positive x-direction. The block initially at rest, accelerates and moves a distance of 10 m in 2 seconds.

1. Calculate the acceleration of the block.
2. Calculate the net force acting on the block.
3. Determine the magnitude of the force exerted by the block on the applied force.

Solution:

1. To calculate the acceleration of the block, we can use the first equation of motion:

   $$v = u + at$$

   Where:

   • $v$ is the final velocity of the block (unknown)
   • $u$ is the initial velocity of the block (0 m/s, as the block is initially at rest)
   • $a$ is the acceleration of the block (unknown)
   • $t$ is the time taken (2 s)

   Rearranging the equation, we have:

   $$v = u + at$$
   $$v = 0 + a \times 2 = 2a$$

   We are given that the block moves a distance of 10 m in 2 seconds. Using the second equation of motion:

   $$s = ut + \frac{1}{2} at^2$$

   We can substitute the known values:

   $$10 = 0 + \frac{1}{2} a \times 2^2$$
   $$10 = 2a$$
   $$a = \frac{10}{2} = 5 \, \text{m/s}^2$$

   Therefore, the acceleration of the block is $5 \, \text{m/s}^2$.

2. To calculate the net force acting on the block, we can use Newton's second law of motion:

   $$F_{\text{net}} = ma$$

   Where:

   • $F_{\text{net}}$ is the net force acting on the block (unknown)
   • $m$ is the mass of the block (2 kg)
   • $a$ is the acceleration of the block (5 m/s^2)

   Substituting the known values:

   $$F_{\text{net}} = 2 \, \text{kg} \times 5 \, \text{m/s}^2 = 10 \, \text{N}$$

   Therefore, the net force acting on the block is $10 \, \text{N}$.

3. To determine the magnitude of the force exerted by the block on the applied force, we can use Newton's third law:

   The force exerted by the block on the applied force is equal in magnitude but opposite in direction to the applied force.

   Therefore, the magnitude of the force exerted by the block on the applied force is $5 \, \text{N}$.

Answer:

1. The acceleration of the block is $5 \, \text{m/s}^2$.
2. The net force acting on the block is $10 \, \text{N}$.
3. The magnitude of the force exerted by the block on the applied force is $5 \, \text{N}$.