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. (3 marks)
mmmmh, can you solve
25t - 80 = 60 ?
To find the times when the magnitude of the velocity is equal to 60 ft/s, we need to set up the equation and solve for t.
Given: v = 25t - 80
1. First, we need to find the magnitude of the velocity. The magnitude is the absolute value or the positive value of v.
|v| = |25t - 80|
2. Next, we set the magnitude of the velocity equal to 60 ft/s:
|25t - 80| = 60
3. Since we have absolute value, we can split the equation into two cases: positive and negative.
Case 1: 25t - 80 = 60
Solving this equation gives:
25t = 140
t = 140/25
t = 5.6 seconds
Case 2: -(25t - 80) = 60
Solving this equation gives:
-25t + 80 = 60
-25t = -20
t = -20/-25
t = 0.8 seconds
4. So, the times when the magnitude of the velocity is equal to 60 ft/s are 5.6 seconds and 0.8 seconds.