Q: A velocity-time graph consists of a rectangle with $$v=2 m/s $$from $$t=0 to$$ $$t=3 s $$and a triangle with base $$3 s $$and height $$4 m/s $$from $$t=3 to$$ $$t=6 s. $$What is the total displacement from $$t=0 to$$ $$t=6 s$$?

$$2 \times 3 + \frac{1}{2} \times 3 \times 4 = 6 + 6 = 12 m$$

Q: A velocity-time graph shows a rectangle above the time axis ($$v=5 m/s$$, $$t=0 to$$ $$t=2 s) $$and a triangle below the time axis (base $$2 s$$, height $$-3 m/s$$, $$t=2 to$$ $$t=4 s). $$What is the net displacement?

$$5 \times 2 + \frac{1}{2} \times 2 \times (-3) = 10 - 3 = 7 m$$

Question 1

In a velocity-time graph, what does the area under the curve between two time points represent?

Accepted Answer

The object's displacement $$\Delta x$$ during that interval

Question 2

Given a velocity-time graph, how do you calculate the displacement $$\Delta x$$ for a time interval where the velocity is negative?

Accepted Answer

Find the area below the time axis and subtract it from the total displacement

Question 3

A moving object has a velocity-time graph that forms a rectangle above the time axis from $$t=0 to$$ $$t=2 s $$with $$v=3 m/s. $$What is the displacement during this interval?

Accepted Answer

$$6 m$$

Question 4

If a velocity-time graph forms a triangle below the time axis from $$t=4 s to$$ $$t=6 s $$with a base of $$2 s $$and a height of $$-2 m/s$$, what is the displacement for this interval?

Accepted Answer

$$-2 m$$

Question 5

A box moves according to the velocity-time graph shown. From $$t=0 to$$ $$t=4 s$$, the area under the curve is $$3 m. $$What does this value represent?

Accepted Answer

The displacement of the box from $$t=0 to$$ $$t=4 s$$

Question 6

For a velocity-time graph, which formula is used to calculate the area of a triangle segment under the curve?

Accepted Answer

$$A = \frac{1}{2} b h$$

Question 7

If the velocity-time graph shows a segment above the time axis and another segment below the time axis, how do you find the total displacement?

Accepted Answer

Subtract the area below the axis from the area above the axis

Question 8

A velocity-time graph for a moving object is a straight line sloping downwards, crossing the time axis at $$t=5 s. $$What does the area above the time axis represent before $$t=5 s$$?

Accepted Answer

Positive displacement $$\Delta x$$

Question 9

If a velocity-time graph shows a constant velocity of $$-4 m/s $$from $$t=6 s to$$ $$t=8 s$$, what is the displacement during this interval?

Accepted Answer

$$-8 m$$

Question 10

A student calculates the area under a velocity-time graph from $$t=0 to$$ $$t=10 s $$and gets $$7 m. $$What does this value indicate?

Accepted Answer

The total displacement $$\Delta x$$ over $$10 s$$

Question 11

Which of the following statements is TRUE regarding the sign of displacement from a velocity-time graph?

Accepted Answer

Areas above the time axis represent positive displacement, and areas below represent negative displacement

Question 12

A velocity-time graph consists of a rectangle with $$v=2 m/s $$from $$t=0 to$$ $$t=3 s $$and a triangle with base $$3 s $$and height $$4 m/s $$from $$t=3 to$$ $$t=6 s. $$What is the total displacement from $$t=0 to$$ $$t=6 s$$?

Accepted Answer

$$2 	imes 3 + \frac{1}{2} 	imes 3 	imes 4 = 6 + 6 = 12 m$$

Question 13

If the velocity-time graph shows a segment with velocity $$v=0 m/s $$for $$5$$ seconds, what is the displacement during this interval?

Accepted Answer

$$0 m$$

Question 14

A velocity-time graph for a car shows a triangle below the time axis from $$t=2 s to$$ $$t=5 s $$with a base of $$3 s $$and a height of $$-6 m/s. $$What is the displacement for this interval?

Accepted Answer

$$-9 m$$

Question 15

Which method is most appropriate for finding the displacement from a velocity-time graph with multiple segments (rectangles and triangles)?

Accepted Answer

Calculate the area of each segment and sum them, considering the sign

Question 16

A velocity-time graph shows a rectangle above the time axis ($$v=5 m/s$$, $$t=0 to$$ $$t=2 s) $$and a triangle below the time axis (base $$2 s$$, height $$-3 m/s$$, $$t=2 to$$ $$t=4 s). $$What is the net displacement?

Accepted Answer

$$5 	imes 2 + \frac{1}{2} 	imes 2 	imes (-3) = 10 - 3 = 7 m$$

Question 17

If a velocity-time graph shows a triangle above the time axis with base $$4 s $$and height $$8 m/s$$, what is the area and what does it represent?

Accepted Answer

$$16 m$$, representing the displacement $$\Delta x$$

Question 18

A velocity-time graph for a runner shows a rectangle ($$v=6 m/s$$, $$t=0 to$$ $$t=3 s) $$and a triangle ($$v$$ decreases to $$0 m/s at$$ $$t=6 s). $$What is the total displacement?

Accepted Answer

$$6 	imes 3 + \frac{1}{2} 	imes 3 	imes 6 = 18 + 9 = 27 m$$

Question 19

Why is the area under a velocity-time graph sometimes negative?

Accepted Answer

Because the velocity is negative, indicating motion in the opposite direction

Displacement from Velocity-Time Graphs: Area Under the Curve

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