The magnitude of the velocity of a car is given by the equation v=|35t-70| where t represents time in seconds and v represents velocity in meters per second. Algebraically determine when the magnitude of velocity is 17.5 m/s.
Can you show steps and answer? this is part of my review(not for marks) for a midterm and I want to be prepared
|35t-70| = 17.5
35t-70 = ±17.5
35t = 70 ± 17.5
t = 2 ± 1/2
To find when the magnitude of velocity is 17.5 m/s, we need to solve the equation v = |35t - 70| for t.
Step 1: Split the equation into two cases based on the absolute value:
Case 1: 35t - 70 = 17.5
Case 2: 35t - 70 = -17.5
Step 2: Solve for t in each case:
Case 1: 35t - 70 = 17.5
Add 70 to both sides:
35t = 87.5
Divide both sides by 35:
t = 87.5 / 35
Simplify:
t = 2.5
Case 2: 35t - 70 = -17.5
Add 70 to both sides:
35t = 52.5
Divide both sides by 35:
t = 52.5 / 35
Simplify:
t = 1.5
Step 3: Check the solutions by substituting them back into the original equation:
For t = 2.5:
v = |35(2.5) - 70|
v = |87.5 - 70|
v = |17.5|
v = 17.5 m/s (magnitude matches)
For t = 1.5:
v = |35(1.5) - 70|
v = |52.5 - 70|
v = |-17.5|
v = 17.5 m/s (magnitude matches)
Therefore, the magnitude of velocity is 17.5 m/s when t = 2.5 seconds and t = 1.5 seconds.
Certainly! Let's find when the magnitude of velocity is 17.5 m/s using the given equation v = |35t - 70|.
Step 1: Start with the equation v = |35t - 70|.
Step 2: Since we are looking for the magnitude of velocity, we can remove the absolute value signs, which means we need to consider two cases: one where the expression inside the absolute value is positive, and another where it is negative.
Case 1: When 35t - 70 is positive.
In this case, the equation becomes v = 35t - 70.
Step 3: Set v equal to 17.5 m/s:
17.5 = 35t - 70
Step 4: Solve for t:
35t = 17.5 + 70
35t = 87.5
t = 87.5/35
t ≈ 2.5 seconds
Case 2: When 35t - 70 is negative.
In this case, the equation becomes v = -(35t - 70).
Step 3: Set v equal to 17.5 m/s:
17.5 = -(35t - 70)
Step 4: Solve for t:
35t - 70 = -17.5
35t = -17.5 + 70
35t = 52.5
t = 52.5/35
t ≈ 1.5 seconds
So, the two solutions are t = 2.5 seconds and t = 1.5 seconds.
Therefore, the magnitude of velocity is 17.5 m/s at approximately t = 2.5 seconds and t = 1.5 seconds.