Graphing at a Glance - AP Physics 1 PDF

Graphing at a Glance - AP Physics 1 Graph What can be calculated/deduced? Position at an instant Displacement in a time interval...

Graphing at a Glance - AP Physics 1 Graph What can be calculated/deduced? Position at an instant Displacement in a time interval Slope at an instant = velocity of the tangent line at that instant direction of velocity → sign of slope Speeding up - curve getting steeper; slowing down - curve getting shallower Sign of acceleration; upward-facing parabola → + acceleration; downward facing parabola → - acceleration If plots of two object’s motion is shown on the same graph, the intersection gives the instant they For a θ 𝑣𝑠 𝑡, graph, replace with cross each other or collide or catch up with each appropriate angular quantities other Velocity at an instant; direction + speed Acceleration at an instant = slope of the tangent line at that instant Displacement in a time interval = area under the graph i.e bounded between the line and the time axis; + area above the time axis and -area under the time axis; total displacement is the sum of the areas keeping the + and - signs; distance is the aum of the absolute values of the areas. If mass 𝑚 is given, 𝐹𝑛𝑒𝑡 = 𝑚𝑎 If mass 𝑚 is given, momentum 𝑝 = 𝑚𝑣 If mass 𝑚 is given, Impulse =∆𝑝 1 2 For a ω 𝑣𝑠 𝑡, graph, replace with If mass 𝑚 is given, 𝐾. 𝐸 = 2 𝑚𝑣 at an instant appropriate angular quantities If mass 𝑚 is given, 𝑊𝑜𝑟𝑘 = ∆𝐾. 𝐸 in an interval If the acceleration and hence net force is constant, then 𝐹𝑛𝑒𝑡 × ∆𝑥 (𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑔𝑟𝑎𝑝ℎ)=𝑊𝑜𝑟𝑘! This observation is attributed to Jacob Wang (2022) If the graph is of the tangential velocity of a rotating object and distance from the center 𝑟 is 𝑣 given, then ω = 𝑟 If plots of two object’s motion from the same point is shown on the same graph, the instant at which area under the graph is the same for both objects is the instant the two objects collide or cross each other Acceleration at an instant Change in velocity ∆𝑣 in an interval Direction of net force if a direction of velocity or a reference direction is given If mass 𝑚 is given, then net force 𝐹𝑛𝑒𝑡 If mass 𝑚 is given, and net force 𝐹𝑛𝑒𝑡 is constant, then change in momentum ∆𝑝 = 𝐹𝑛𝑒𝑡∆𝑡, where ∆𝑡 is the time duration of constant force If velocity 𝑣 at two instants can be found then, 1 2 For a α 𝑣𝑠 𝑡, graph, replace with change in 𝐾. 𝐸 = ∆( 2 𝑚𝑣 ) appropriate angular quantities Graphing at a Glance - AP Physics 1 Force at a specific location If mass 𝑚 is given, acceleration at a specific location Area under the graph gives 𝑤𝑜𝑟𝑘 𝑊 = ∆𝐾. 𝐸; may be positive (𝐾. 𝐸 ↑) or negative (𝐾. 𝐸 ↓) If mass 𝑚 initial velocity 𝑣𝑖 is known, 𝑣𝑓 can be found (magnitude only; direction requires additional information to be taken into account). Force at an instant If mass 𝑚 is given, acceleration at an instant Area under the graph gives 𝐼𝑚𝑝𝑢𝑙𝑠𝑒 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑝; may be positive (𝑝 ↑) or negative (𝑝 ↓) If mass 𝑚 initial velocity 𝑣𝑖 is known, 𝑣𝑓 can be found (magnitude and direction). If the graph depicts force experienced by object 1 during a collision; then the force on object 2 is the vertically flipped image of the given graph Momentum at an instant; velocity if mass is given Slope of the tangent line = Force at an instant If graph shows momentum values of two objects during collision, then total momentum can be calculated; momentum conservation can be checked; Time duration of collision can be found; whether the collision is elastic (𝐾. 𝐸 𝑐𝑜𝑛𝑠𝑒𝑟𝑣𝑒𝑑) or not can be confirmed Acceleration for some value of 𝐹, linear trend of graph may be extrapolated ∆𝑎 1 Since 𝐹𝑛𝑒𝑡 = 𝑚𝑎, ∆𝐹 = 𝑠𝑙𝑜𝑝𝑒 = 𝑚(𝑚𝑎𝑠𝑠) ; take 𝑛𝑒𝑡 the reciprocal to get mass The 𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝐹 that causes acceleration = resistive force (for example friction) If 𝐹(𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑎𝑥𝑖𝑠) 𝑣𝑠 𝑎(ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑎𝑥𝑖𝑠)graph is given, slope = 𝑚𝑎𝑠𝑠 𝑚 Graphing at a Glance - AP Physics 1 If the total mechanical energy is conserved, knowing either 𝐾. 𝐸 or 𝑃. 𝐸 allows you to find the other If 𝐾. 𝐸 is known, and mass 𝑚 is given, 𝑣 can be found If, 𝑃. 𝐸 = 𝑚𝑔ℎ, the graph of 𝑃. 𝐸 𝑣𝑠 ℎ is linear If the 𝑃. 𝐸 𝑔𝑟𝑎𝑝ℎ 𝑖𝑠 𝑙𝑖𝑛𝑒𝑎𝑟, 𝑠𝑜 𝑖𝑠 𝑡ℎ𝑒 𝐾. 𝐸 𝑔𝑟𝑎𝑝ℎ; If the total mechanical energy is conserved, knowing either 𝐾. 𝐸 or 𝑃. 𝐸 allows you to find the other If 𝐾. 𝐸 is known, and mass 𝑚 is given, 𝑣 can be found The time dependence of height is typically quadratic, so the 𝑃. 𝐸 graph vs 𝑡𝑖𝑚𝑒 is not likely to be linear Graphing in Oscillations