Following graphs show position as a function of time for a particle that moves a
ID: 1759291 • Letter: F
Question
Following graphs show position as a function of time for a particle that moves along the x axis. Select the graphs that at t = 1 s (the vertical hash mark across the x - axis is one second), fit the following situations. (a) zero velocity and positive acceleration graph 6 graph 3 graph 2 graph 4 graph 5 graph 7 graph 1 graph 8 (b) zero velocity and negative acceleration graph 5 graph 3 graph 4 graph 2 graph 8 graph 7 graph 1 graph 6 (c) negative velocity and positive acceleration graph 1 graph 6 graph 7 graph 3 graph 5 graph 2 graph 8 graph 4 (d) negative velocity and negative acceleration. graph 8 graph 6 graph 2 graph 5 graph 3 graph 7 graph 1 graph 4 (e) In which graph(s) would the speed of the particle be increasing and not zero at t = 1 s? graph 5 graph 6 graph 1 graph 3 graph 7 graph 8 graph 2 graph 4 The velocity function is the time derivative of the position function. The particle stops and turns around when the velocity is zero (the position is an extreme value then). Acceleration is the time derivative of the velocity function. The velocity reaches an extreme value when its derivative (the acceleration) is zero.Explanation / Answer
graph 1: zero velocity and positive acceleration graph 2: zero velocity and negative acceleration graph 3: zero velocity and zero acceleration graph 4: negative velocity and negative acceleration graph 5: positive velocity and zero acceleration graph 6: negative velocity and positive acceleration graph 7: same as graph 3 graph 8: positive velocity and negative acceleration Part A) "zero velocity" means that the slope of the line will be zero(first derivative is zero at t=1). "positive acceleration" means that the second derivative ispositive and the shape of the line will be concave up (secondderivative is positive at t=1) this matches graph 1 Part B) "zero velocity" means that the slope of the line will be zero(first derivative is zero at t=1). "negative acceleration" means that the second derivative isnegative and the shape of the line will be concave down (secondderivative is negative at t=1) this matches graph 2 Part C) "negative velocity" means that the slope of the line will benegative (first derivative is negative at t=1). "positive acceleration" means that the second derivative ispositive and the shape of the line will be concave up (secondderivative is positive at t=1) this matches graph 6 Part D) "negative velocity" means that the slope of the line will benegative (first derivative is negative at t=1). "negative acceleration" means that the second derivative is negatveand the shape of the line will be concave down (second derivativeis negative at t=1) this matches graph 4 Part E) "speed increasing and not zero" is positive acceleration andnonzero velocity. this matches graph 6