The velocity of an object is given by the formula v=25t-80, where the time is expressed in seconds and the velocity is expressed in feet per second. Find the times when the magnitude of the velocity is equal to 60 ft/s
To find the times when the magnitude of the velocity is equal to 60 ft/s, we need to solve the equation:
|v| = 60
Since the velocity equation is given as v = 25t - 80, we can rewrite the equation as:
|25t - 80| = 60
To solve this equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
1. Case 1: 25t - 80 > 0
Solve for t:
25t - 80 = 60
Adding 80 to both sides:
25t = 140
Dividing both sides by 25:
t = 5.6
2. Case 2: 25t - 80 < 0
Solve for t:
-(25t - 80) = 60
Expanding the expression:
-25t + 80 = 60
Subtracting 80 from both sides:
-25t = -20
Dividing both sides by -25:
t = 0.8
Therefore, the times when the magnitude of the velocity is equal to 60 ft/s are t = 0.8 seconds and t = 5.6 seconds.
To find the times when the magnitude of the velocity is equal to 60 ft/s, we can set the magnitude of the velocity equal to 60 and solve for t.
The magnitude of the velocity is given by the absolute value of the velocity, so we have:
|v| = 60
Substituting the given equation for v, we have:
|25t - 80| = 60
To solve this equation, we can break it into two cases:
Case 1: 25t - 80 = 60
Solving for t, we get:
25t = 60 + 80
25t = 140
t = 140/25
t = 5.6 seconds
Case 2: -(25t - 80) = 60
Simplifying this equation, we get:
-25t + 80 = 60
-25t = 60 - 80
-25t = -20
t = -20/-25
t = 0.8 seconds
Therefore, the times when the magnitude of the velocity is equal to 60 ft/s are t = 5.6 seconds and t = 0.8 seconds.
wouldn't you you just set
25t - 80 = 60 and solve ?
looks pretty straighforward