19. The velocity of an object fired directly upward is given by V = 35 – 9.8t, where t is time in seconds. Which inequality describes the velocity when t is between 0.5 and 1.5 seconds? (HINT: Remember that when you multiply an inequality by a negative number, you must switch the direction of the inequality.)
Please explain how to do
v(0.5) = 30.1
v(1.5) = 20.3
So, 20.3 <= v <= 30.1
not sure why the warning about negative quantities ...
To determine the inequality that describes the velocity when t is between 0.5 and 1.5 seconds, we need to substitute the given values of t into the equation V = 35 - 9.8t and see what the velocity values are.
First, let's substitute t = 0.5 into the equation:
V = 35 - 9.8(0.5)
V = 35 - 4.9
V = 30.1
Next, let's substitute t = 1.5 into the equation:
V = 35 - 9.8(1.5)
V = 35 - 14.7
V = 20.3
Now that we have two velocity values, we can determine the relationship between them by comparing them. In this case, we know that the velocity is decreasing over time because of the negative coefficient (-9.8) of t in the equation. Therefore, we can write the inequality as:
30.1 ≥ V ≥ 20.3
However, we need to keep in mind the hint provided, which states that when multiplying an inequality by a negative number, we must switch the direction of the inequality. In this case, we have a negative coefficient (-9.8) multiplying t, so we need to flip the inequality. The correct inequality would be:
20.3 ≤ V ≤ 30.1
Therefore, the inequality that describes the velocity when t is between 0.5 and 1.5 seconds is 20.3 ≤ V ≤ 30.1.
To find the inequality that describes the velocity when t is between 0.5 and 1.5 seconds, we need to substitute the given values of t into the equation V = 35 – 9.8t and compare the results.
First, let's substitute t = 0.5 into the equation:
V = 35 - 9.8(0.5)
V = 35 - 4.9
V = 30.1
Now, let's substitute t = 1.5 into the equation:
V = 35 - 9.8(1.5)
V = 35 - 14.7
V = 20.3
So, when t is 0.5 seconds, the velocity is 30.1, and when t is 1.5 seconds, the velocity is 20.3.
Now, we need to determine the direction of the inequality. The coefficient of t in the equation V = 35 – 9.8t is -9.8, which is negative. When multiplying an inequality by a negative number, we must switch the direction of the inequality.
Since we are looking for values between 0.5 and 1.5 seconds, the inequality should be greater than the velocity at 1.5 seconds and less than the velocity at 0.5 seconds.
Therefore, the inequality that describes the velocity when t is between 0.5 and 1.5 seconds is:
20.3 < V < 30.1