51. A balloon starts rising from the ground, vertically upwards, uniformly at the rate of 1 m s-1. At the end of 4 seconds, a bo
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6) b) 2.7 m/s
7) b) DCA
8) b) B
Explanation:
6)
In a displacement-time plot, the slope of the line is given by
where
is the change in the y-variable, so it is the displacement
is the change in the x-variable, so it is the time elapsed
So, the slope of the line in a displacement-time plot corresponds to the velocity:
Therefore, to find the velocity of the object, we have to estimate the slope of its curve.
To estimate the velocity of object B, we have to estimate the slope of the line tangent to curve B at 10 seconds.
By doing an estimate by eye, we see that the displacement of object B changes from -10 m to 0 m when time increases from about 8 s to 12 s, so the velocity is about:
So the closest option is b) 2.7 m/s.
7)
As we said in part A, the velocity of each object is given by the slope of each curve.
Therefore:
- The steeper the curve, the higher the velocity
- The less steep the curve, the lower the velocity
From the graph, we observe that, among A, C and D:
- Curve D has the largest slope (in absolute value), so object D has the largest magnitude of the velocity
- Curve C is less steep than curve C, so object C has the second largest magnitude of velocity
- Curve A is flat, so the slope is zero, so its velocity is zero
So, from greatest magnitude to lowest magnitude of velocity, we have:
b) DCA
8)
In the graph, the overall displacement of each object is given by the change in the y-variable, .
This means that the object with largest displacement is the object whose curve has the largest variation in y.
From the graph, we see that:
- Object b has the largest variation in y, from -15 m to 30 m, so
- Then, object D has the second largest displacement (in magnitude), from -15 m to 25 m,
Finally, object C has displacement
While object A has displacement zero. Therefore, the correct option is
b) B