Displacement, Velocity & Acceleration (College Board AP® Physics 1: Algebra-Based): Free Response Questions

Figure 1

A long track, inclined at an angle $\theta$ to the horizontal, has small speed bumps on it. The bumps are evenly spaced a distance $d$ apart, as shown in Figure 1. The track is actually much longer than shown, with over 100 bumps. A cart of mass $M$ is released from rest at the top of the track. A student notices that after reaching the 40th bump the cart's average speed between successive bumps no longer increases, reaching a maximum value $v_{avg}$. This means the time interval taken to move from one bump to the next bump becomes constant.

Consider the cart's motion between bump 41 and bump 44.

On the axes shown in Figure 2:

i) Sketch a graph of the cart's velocity $v$ as a function of time from the moment it reaches bump 41 until it reaches bump 44.

ii) Sketch and label a dashed horizontal line at $v=v_{avg}$ over the same time interval.

Figure 2

Derive an expression for the time interval $T$ taken for the cart to travel between two successive bumps. Write your expression in terms of $d$, $v_{min}$, $v_{max}$ and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

One end of an elastic climbing rope is fixed to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible. 

The full length of the rope is 60.0 m. From position A to B, the block falls freely with acceleration $a$. 

Identify whether the acceleration $a$ of the block is less than, equal to, or greater than $g$.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ $a<g$‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ $a=g$ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ $a>g$

Justify your reasoning.

Between positions B and C, the resultant force on the block changes because the tension in the rope increases as the rope extends. 

A student makes the following claim:

"A kinematic equation can be used to find the vertical velocity of the lock at position B."

Identify whether the student's claim is correct or incorrect.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ correct ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ incorrect

Justify your answer.

Figure 1

Figure 1 shows the flight path of a drone conducting a LiDAR (Light Detection and Ranging) scan of a ranch in Utah. The drone takes off from the point marked ×. It flies a grid pattern of 500 m horizontal passes, shifting 50 m to the north (toward the top of Figure 1) between passes.

After its final pass, the drone flies directly south, back to the point marked ×, where it lands.

Estimate the distance covered by the drone during its flight.

Determine the displacement of the drone for its whole flight. Justify your answer.

A sprinter runs a $200\mathrm{m}$ race. Starting from rest, the sprinter covers $20\mathrm{m}$ in $4\mathrm{s}$ and accelerates at a constant rate. The remaining distance is covered at a constant velocity equal to that which the sprinter had at the end of their period of acceleration.

Determine the total time required by the sprinter to complete the race.

On the axes provided in Figure 1, sketch a graph of the position of the sprinter as a function of time.