Unit 1 · Accelerated launch and projectile motion · Accelerated launch and projectile motion
A cart starts from rest on a horizontal track and accelerates uniformly at magnitude \(a\) for time \(T\). It then leaves the edge of a table of height \(h\) horizontally. Air resistance is negligible. (a) Derive the cart's speed and displacement while it is on the track. (b) Derive the time of flight and horizontal range after it leaves the table. (c) Derive the magnitude and direction of the velocity immediately before impact. (d) If the track acceleration is doubled while \(T\) and \(h\) are unchanged, determine the factor by which the range and impact-speed components change.
Write your answer on paper, showing your working. Compare it with the solution and point allocation when ready.
MCQ · Easy · 1 pointCalculator: allowed
Unit 1 · Acceleration · Acceleration
A car moving at \(20\text{ m/s}\) comes to rest with constant acceleration in \(5.0\text{ s}\). What is its acceleration?
FRQ · Hard · 10 pointsCalculator: allowed
Unit 1 · Acceleration from position-time data · Acceleration from position-time data
Students investigate whether a cart has constant acceleration while rolling from rest down a ramp. They have a cart, adjustable ramp, meterstick, motion sensor, and computer. (a) Describe a procedure that produces position and time measurements suitable for determining acceleration, including steps that reduce random error. (b) Starting from a constant-acceleration relation, identify quantities for a linearized graph and state how its slope gives acceleration. (c) The best-fit slope of the proposed graph is \(0.72\text{ m/s}^2\). Determine the acceleration. (d) Describe one graph-based check of the constant-acceleration model. (e) A sensor reports every position \(1.5\text{ cm}\) too large. Determine whether this offset changes the measured acceleration and justify.
Write your answer on paper, showing your working. Compare it with the solution and point allocation when ready.
MCQ · Easy · 1 pointCalculator: allowed
Unit 1 · Area under a velocity-time graph · Area under a velocity-time graph
A velocity-time graph rises linearly from zero to \(6\text{ m/s}\) during the first \(2\text{ s}\), then remains at \(6\text{ m/s}\) for another \(3\text{ s}\). What is the total displacement?
MCQ · Medium · 1 pointCalculator: allowed
Unit 1 · Area under a velocity-time graph · Area under a velocity-time graph
A velocity-time graph rises linearly from zero to \(8\text{ m/s}\) during the first \(3\text{ s}\), then remains at \(8\text{ m/s}\) for another \(2\text{ s}\). What is the total displacement?
MCQ · Hard · 1 pointCalculator: allowed
Unit 1 · Average velocity on a closed path · Average velocity on a closed path
A runner completes one full \(400\text{ m}\) lap in \(64\text{ s}\) and returns to the starting line. What is the runner's average velocity?
MCQ · Easy · 1 pointCalculator: allowed
Unit 1 · Average velocity on a closed path · Average velocity on a closed path
A drone completes two full laps of a closed course in \(80\text{ s}\) and returns to its starting point. What is its average velocity for the trip?
FRQ · Hard · 8 pointsCalculator: allowed
Unit 1 · Comparing velocity-time motions · Comparing velocity-time motions
Objects A and B start at the same position at \(t=0\). Object A moves at constant velocity \(v_0\) from \(0\) to \(2T\). Object B starts from rest, accelerates uniformly to \(v_0\) during \(0<t<T\), and then moves at \(v_0\) until \(2T\). (a) Compare their accelerations during each interval. (b) Calculate each displacement from \(0\) to \(2T\). (c) Determine their separation at \(2T\) and state which is ahead. (d) Sketch both position-time graphs and explain how slope and concavity encode the velocity descriptions.
Write your answer on paper, showing your working. Compare it with the solution and point allocation when ready.
MCQ · Medium · 1 pointCalculator: allowed
Unit 1 · Constant-acceleration stopping distance · Constant-acceleration stopping distance
A car moving at \(20\text{ m/s}\) slows uniformly at \(4\text{ m/s}^2\) until it stops. How far does it travel while stopping?
MCQ · Medium · 1 pointCalculator: allowed
Unit 1 · Constant-acceleration velocity · Constant-acceleration velocity
A delivery robot moves along a straight aisle with initial velocity \(3\text{ m/s}\) and constant acceleration \(2\text{ m/s}^2\) for \(4\text{ s}\). What is its final velocity?