An object moves along the x axis,with its position given by the function x(t)= ½ t³.Which of the following can be obtained from a graph of x vs.t? A)The velocity of the object at any instant in time B)The displacement of the object during a specified time interval C)The speed of the particle at any instant in time D)The average velocity of the object during as specified time interval E)All of the above

Question

Quizplus · Accepted Answer

A graph of x vs. t is a position vs. time graph, and from this graph, we can obtain all of the listed quantities. 
Velocity is given by the slope of the tangent line to the position vs. time graph at any given point, so we can determine the velocity at any instant in time from the graph. 
Displacement is the change in position over a specified time interval, which can be found by calculating the area under the velocity vs. time graph within that time interval. 
Speed is the absolute value of velocity, so we can obtain this from the same tangent lines used to find velocity. 
Average velocity can be found by calculating the slope of the line connecting two points on the position vs. time graph, representing the object's average displacement over a specified time interval. Therefore, all of the listed options can be obtained from a graph of x vs. t.

​An Object Moves Along the X Axis,with Its Position Given

An Object Moves Along the X Axis,with Its Position Given