Question

lesson 8 | session 1
3 a marine biologist is studying how fast a dolphin swims. the dolphin swims at a constant speed for 5 seconds. the distance it swims is 55 meters. the relationship between time and distance for the trip is proportional.
a. make a graph showing the change in the dolphins distance over time. how far does the dolphin swim in 1 second? show your work.
b. check your answer to problem 3a. show your work.

Explanation:

Step1: Find the speed formula

Speed $v=\frac{d}{t}$, where $d$ is distance and $t$ is time.

Step2: Substitute given values

Given $d = 55$ meters and $t = 5$ seconds, so $v=\frac{55}{5}$.

Step3: Calculate the speed

$v = 11$ meters per second. So the dolphin swims 11 meters in 1 second.

To graph:

• The independent variable is time $t$ (in seconds) and is plotted on the x - axis.
• The dependent variable is distance $d$ (in meters) and is plotted on the y - axis.
• We have the points $(0,0)$ (at time $t = 0$, distance $d=0$) and $(5,55)$. Since the relationship is proportional, the graph is a straight - line passing through the origin with a slope of 11.

Step4: Check the answer

If the speed $v = 11$ m/s, then in 5 seconds, the distance $d=v\times t$. Substituting $v = 11$ m/s and $t = 5$ s, we get $d=11\times5=55$ meters, which is the original distance given.

Answer:

a. The dolphin swims 11 meters in 1 second.
b. As shown above, when using the calculated speed of 11 m/s to find the distance in 5 seconds, we get 55 meters which matches the given distance, so the answer in part a is correct.