Comparing motions of multiple objects - Question 7
(A) Modulus: moderate and low slopes, (B) Stas: Up, down, large up slopes, (C) Kinet: Up, down, low up, (D) Terek: Single up slope
Looking at the speed-time graphs of the four aliens:
Calculating slopes:
We can calculate the slopes mathematically. As you probably remember from your math classes, slope is rise/run.
Between 4 and 12 seconds, Stas’ speed increases from 0 m/s to 100 m/s. Thus, the rise is [100 m/s - 0 m/s] = 100 m/s. The run is [12 s - 4 s] = 8 s. Therefore, the slope is 100 m/s divided by 8 s = 12.5 m/s/s. This number (the value of the slope) is also the rate of increase in speed. Therefore, between 4 seconds and 12 seconds, Stas’ speed increases at the rate of 12.5 m/s each second.
For Kinet and Modulus, between 0 s and 3 s the speed-time graphs are essentially the same. The rise is (about) [28 m/s - 0 m/s] = 28 m/s. The run is 3 s. Therefore, the slope is rise/run = 28 m/s divided by 3 s = 9.3 m/s/s. This means that during the first three seconds, the speeds of both Kinet and Modulus increased at a rate of 9.3 m/s each second. This is smaller than the rate for Stas.
Transcript / Long description
Representing Motion on Speed-Time Graphs – Comparing motions of multiple objects
Looking at the speed-time graphs of the four aliens, who shows the greatest rate of speeding up? (Be able to identify the time period during which the rate is the greatest.)
Feedback: The best answer would be Stas. Between 4 seconds and 12 seconds the slope of its speed-time graph is greater (although not by very much) than the slopes of the speed-time graphs during the first 3 seconds for Kinet and Modulus. This means that Stas’ rate of increase in speed is greater than the rate of increase for either Kinet or Modulus.
To be precise, we can calculate the slopes mathematically. As you probably remember from your math classes, slope is rise/run. Between 4 and 12 seconds, Stas’ speed increases from 0 m/s to 100 m/s. Thus, the rise is [100 m/s - 0 m/s] = 100 m/s. The run is [12 s - 4 s] = 8 s. Therefore, the slope is 100 m/s divided by 8 s = 12.5 m/s/s. This number (the value of the slope) is also the rate of increase in speed. Therefore, between 4 seconds and 12 seconds, Stas’ speed increases at the rate of 12.5 m/s each second.
For Kinet and Modulus, between 0 s and 3 s the speed-time graphs are essentially the same. The rise is (about) [28 m/s - 0 m/s] = 28 m/s. The run is 3 s. Therefore, the slope is rise/run = 28 m/s divided by 3 s = 9.3 m/s/s. This means that during the first three seconds, the speeds of both Kinet and Modulus increased at a rate of 9.3 m/s each second. This is smaller than the rate for Stas.
