🎡AP Physics 1
2. A student rolls a small cart along a straight track that lies on a level laboratory floor.
Figure 1. Velocity components of the cart versus time as measured by observer A for the first 6.0 s of motion.
Figure 2. Two instants for drawing the cart’s velocity vectors and the (constant) acceleration vector as measured by observer A.
Draw and label, in Figure 2, the velocity vectors of the cart at and at , as measured by observer A. Figure 1 shows the x- and y-components of the cart's velocity as functions of time as measured by observer A. The cart's acceleration is constant from to .
• Each vector must have a magnitude and direction consistent with Figure 1.
• Also draw and label the cart's acceleration vector (which is the same at both times).
• Your vectors must be drawn with correct relative lengths within each panel.
Figure 3. Observer A’s coordinate system and a blank set of axes for sketching the cart’s trajectory from 0 to 6.0 s.
Starting with definitions of average velocity and average acceleration, derive expressions for the cart's displacement components and from to . Express your answers in terms of the initial and final velocity components from Figure 1 and the time interval . Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Using Figure 3, sketch the cart's trajectory. The cart starts at the origin of observer A's coordinate system at . The velocity components measured by A are given by Figure 1.
Figure 4. Blank axes for sketching the x-component of the cart’s velocity versus time as measured by observer B, v_xB(t), from 0 to 6.0 s.
Figure 5. Blank axes for sketching the y-component of the cart’s velocity versus time as measured by observer B, v_yB(t), from 0 to 6.0 s.
Observer B moves relative to observer A with constant velocity . Assume both observers use axes that are always parallel (no rotation) and use the same time coordinate. Figure 4 and Figure 5 are blank graphs for the velocity components measured by observer B.
Sketch and label in Figure 4 the graph of from to .
Sketch and label in Figure 5 the graph of from to .
Figure 6. Reference diagram indicating observer B’s motion relative to the laboratory (+x direction) and a workspace to compare the cart’s speeds at t = 1.0 s and t = 5.0 s in observer B’s frame.
Indicate whether the speed of the cart at is greater than, less than, or equal to the speed of the cart at , as measured by observer B. Using your sketched graphs in part C, compare the cart's speed as measured by observer B at two different times: and . Figure 6 shows the relative motion of the observers.
Justify how your response is consistent with the velocity-component graphs you sketched in part C, including how the perpendicular components combine to produce the speed.
