Open Question
FIGURE EX2.8 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat?
2. 1D Motion / Kinematics
Calculating Displacement from Velocity-Time Graphs
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A moving box's motion is described by the velocity graph below. The box's initial position is x = 0.
(a) How far has the box moved at t = 4?
(b) What is the displacement of the box from t=4 to t=10?
A
(a) 16 m;
(b) 0 m
(b) 0 m
B
(a) 16 m;
(b) 24 m
(b) 24 m
C
(a) 24 m;
(b) 0 m
(b) 0 m
D
(a) 24 m;
(b) 24 m
(b) 24 m
E
(a) 32 m;
(b) 0 m
(b) 0 m
F
(a) 32 m;
(b) 24 m
(b) 24 m
Verified step by step guidance1
To find how far the box has moved at t = 4, calculate the area under the velocity-time graph from t = 0 to t = 4. This area represents the distance traveled.
The graph from t = 0 to t = 4 is a triangle with a base of 4 seconds and a height of 8 m/s. Use the formula for the area of a triangle: Area = 0.5 * base * height.
Calculate the area of the triangle from t = 0 to t = 4 to find the distance traveled by the box.
To find the displacement of the box from t = 4 to t = 10, calculate the area under the velocity-time graph from t = 4 to t = 10. Note that the area below the time axis (negative velocity) will be subtracted from the area above the time axis (positive velocity).
The graph from t = 4 to t = 10 forms a trapezoid. Calculate the area of this trapezoid by dividing it into a triangle and a rectangle, then sum the areas, considering the sign of the velocity.
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