AP Physics C Mechanics 1.3: Representing Motion

Represent motion with diagrams, graphs, equations, and narratives, connecting position, velocity, and acceleration through calculus-based kinematics.

[Maximum number: 1]

Scientists have created a new type of lightweight foam and are performing experiments to investigate the properties of the foam. The mass of Cart A is 1000 kg and the mass of Cart B is 2000 kg. A piece of foam with negligible mass is attached to the front of Cart A, as shown. Cart A moves with a constant speed toward Cart B, which is initially at rest. At time $t=0 \mathrm{~s}$ , the foam connected to Cart A makes contact with Cart B. The foam remains in contact with Cart B for 0.5 s, after which the carts separate and both carts move with constant velocities.

Figure for Question 1.3.A—Describe the position, velocity, and acceleration of an object using representations of that object’s motion question 1 — AP Physics C: Mechanics

The graph shows the velocity v of Cart A as a function of time t for the time interval when the foam and Cart B are in contact.

What feature(s) of the graph could be used to estimate the displacement of Cart A during the collision?

Using the information shown in the graph, determine the speed of Cart B at $t=0.5 \mathrm{~s}$ .

On the following grid, draw a smooth curve of the velocity of Cart B as a function of time.

(i)

For stating that the area bounded by the curve is the displacement

1 point

(a)(ii)

For indicating momentum is conserved

1 point

Example Response

$\Sigma p_0=\Sigma p_f$

For the correct answer for speed with units (2 m/s)

1 point

Example Solution

$m_{\mathrm A}v_{\mathrm{A0}}+m_{\mathrm B}v_{\mathrm{B0}}=m_{\mathrm A}v_{\mathrm{Af}}+m_{\mathrm B}v_{\mathrm{Bf}}$ $m_{\mathrm A}v_{\mathrm{A0}}-m_{\mathrm A}v_{\mathrm{Af}}=m_{\mathrm B}v_{\mathrm{Bf}}$ $v_{\mathrm{Bf}}=\frac{m_{\mathrm A}}{m_{\mathrm B}}\left(v_{\mathrm{A0}}-v_{\mathrm{Af}}\right)$ $v_{\mathrm{Bf}}=\frac{1000\,\mathrm{kg}}{2000\,\mathrm{kg}}(5\,\mathrm{m/s}-1\,\mathrm{m/s})$ $\therefore v_{\mathrm{Bf}}=2\,\mathrm{m/s}$

For a graph that starts at (0,0) and ends at (0.5,2) or value consistent with (a)(ii)

1 point

For a smooth, continuous curve that transitions from concave up to concave down

1 point

Example Solution

$v(\mathrm{m/s})$ $v(\mathrm{m/s})$

Total for part (a)

5 points

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1.3.A—Describe the position, velocity, and acceleration of an object using representations of that object’s motion question 1