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?

Question

Velocity-time graph showing blood flow in the aorta during one heartbeat, with time in seconds and velocity in m/s.

Accepted Answer

Mhm Hey, everyone in this problem, we're told that a boat comes to a stop due to a malfunctioning engine. The velocity versus time graph of the bow would look like the graph below. We're asked to determine the approximate distance the boat moves in meters before it stops. Now, we're given this graph velocity versus time. OK. So we have time in seconds on the X axis. The velocity in meters per second on the Y axis from 0 to 2 seconds. The velocity is zero m per second. It then increases from two seconds to eight seconds to a velocity of 20 m per second. It then decreases from 20 m per second. Back down to zero m per second at 16 seconds and then stays at zero m per second from 16 seconds to 20 seconds. We're given four answer choices. Option A 65 m, option B 88 m, option C 140 m and option D 110 m. Now, we're amplifying distance the boat travels, we're given a velocity versus time curve. So let's recall the relationship between velocity and displacement. The velocity is equal to the derivative of the displacement with respect to time. So V is equal to D X by D T. This means when we have a velocity time curve that delta X, the displacement is going to be equal to the area under R V T Kirk. So in order to figure out the distance of the boat moves before it stops, we just need to find the area under a curve. Now from 0 to 2 seconds, the velocity is zero. So the area under that is just zero. Ok? There's nothing there and there's no height same from 16 to 20 seconds. So what we really need to do is look at this area between two seconds and 16 seconds. And this area makes a triangle. And so the area under the curve is going to be equal to one half multiplied by the base multiplied by the height. Ok? The area of a triangle. So it's gonna be one half. Now the base, it goes up to 16 seconds and it starts at two seconds. So it's gonna be 16 seconds minus two seconds. And similarly, for our height goes up to 20 m per second, starting at zero m per second. So we have 20 m per second minus zero m per second. This tells us that our area is equal to one half multiplied by 14 seconds, multiplied by 20 m per second. And if we work this out, we get a distance traveled of 140 m. All right. So the boat is going to travel 140 m before coming to a stop. This corresponds with answer choice C that's it for this one. Thanks everyone for watching. I hope this video helped.

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?

Verified video answer for a similar problem:

Key Concepts

Velocity-Time Graph

Area Under the Curve

Units of Measurement