AP Physics C Mechanics 1.3 Motion Models Overview

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 Representing 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

All question bank results loaded

Covered syllabus points

1.3 Representing Motion question 1