1D Kinematics Audio Guided Solution K11Q4

Problem Set K11, Question 4:

After driving past the Speed Zone, Cedric accelerates uniformly for 6.0 seconds. The velocity-time graph represents his motion. Use the graph to determine his displacement during these 6.0 seconds of motion.

Audio Guided Solution

This problem represents the motion of an object by a velocity time graph, and the problem asks us to determine the acceleration of the object. On a velocity time graph, the slope of the line is representative of the acceleration, so to determine the answer, what we'll have to do is a rise over run calculation, or a delta y over delta x calculation for the line that we see. That means we need to know two coordinates for that line, and the best points to know the coordinates of are the beginning point at 0 seconds and the end point at 6 seconds. I notice the dashed lines going over to the horizontal and vertical axes here at the 6 second mark, and so at 6 seconds, the y coordinate, or velocity coordinate, is 4 meters per second. So 6, 4 is one of my coordinates points, and the other coordinate point is at 0 seconds. I know that point, those coordinates, to be 0 seconds and 18 meters per second. So now I need to do a rise over run, so I can do 18 minus 4 all over 0 minus 6. 18 minus 4 is 14, and divided by 6, or negative 6, is going to get me a negative slope, and that's consistent with the fact that this line is sloping downwards to the right as opposed to upwards while going to the right. So enter a negative number as your answer. Now one caution here, it's very tempting and a very common wrong answer to do 6 divided by 4, just to go a y value divided by an x coordinate value, and you don't want to do that. You always want to think slope is delta y over delta x. For this type of graph, it gets you a delta velocity over a delta time, and that's how we define acceleration. You can do it.

Solution

Habits of an Effective Problem Solver

An effective problem solver by habit approaches a physics problem in a manner that reflects a collection of disciplined habits. An effective problem-solver...

...reads the problem carefully and develops a mental picture of the physical situation. If needed, they sketch a simple diagram of the physical situation to help visualize it.
...identifies the known and unknown quantities in an organized manner, often times recording them on the diagram itself. They equate given values to the symbols used to represent the corresponding quantites (e.g., v_o = 0 m/s; a = 4.2 m/s/s; v_f = 22.9 m/s; d = ???.).
...plots a strategy for solving for the unknown quantity; the strategy will typically center around the use of physics equations and be heavily dependent upon an understanding of physics principles.
...identifies the appropriate formula(s) to use, often times writing them down. Where needed, they perform the needed conversion of quantities into the proper unit.
...performs substitutions and algebraic manipulations in order to solve for the unknown quantity.

Read About It!

Get more information on the topic of 1-Dimensional Kinematics at The Physics Classroom Tutorial.

Determining the Area on a v-t Graph

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Try our YouTube video on the topic of ...

Determining the Displacement from a Velocity-Time Graph