Question Video: Finding the Displacemnt from a Velocity-Time Graph

The figure shown is a velocity–time graph for a body moving in a straight line. Determine the deceleration of the body during the final section of its movement, given that it came to rest 100 seconds after it started moving.

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Video Transcript

The figure shown is a velocity–time graph for a body moving in a straight line. Determine the deceleration of the body during the final section of its movement, given that it came to rest 100 seconds after it started moving.

We know that the acceleration on a velocity–time graph is equal to its slope or gradient. We can therefore calculate the acceleration at any point by dividing the change in velocity by the change in time. In this question, our velocity is measured in meters per second, and our time is measured in seconds. Dividing meters per second by seconds gives us meters per second per second. This is written as meters per second squared or meters per square second.

When the slope or gradient of our graph is positive, the body will be accelerating. When the slope or gradient of the graph is negative, the body will be decelerating. Finally, if a line on our velocity–time graph is horizontal, the acceleration will be equal to zero and the body will be traveling with a constant velocity. In this question, we’re interested in the deceleration in the final section of the graph. This occurs between 90 seconds and 100 seconds. The velocity during this time period has decreased from 45 meters per second to zero meters per second. This means that our change in velocity is zero minus 45.

As mentioned, the time period goes from 90 seconds to 100 seconds. Therefore, the change in time is 100 minus 90. This can be simplified to negative 45 over 10. When dividing by 10, we move all our digits one place to the right. And dividing a negative number by a positive gives a negative answer. The acceleration of the body is therefore negative 4.5 meters per square second. The deceleration will be the absolute value or modulus of this. This is equal to 4.5 meters per square second.

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