A car travels for 10 minutes. it's velocity is given by v=960t-5t, where t is in minutes and v is in ft/min. Find the maximum speed in ft/min during those minutes.
Please help I have no idea how to solve this problem.
First, I doubt that 960t-5t is correct.
If you meant v=960-5t, then clearly 960 is its maximum speed, whence it slowed down.
If you meant v=960t-5t^2, that's a bit more interesting. Then the maximum speed is at t=96, and v(96) = 46080
But, if we stop counting at t=10, then the max speed is at t=10.
I think the problem has been garbled.
Oops sorry It is supposed to be v=960t-5t^3
Wouldn't the max still be at t=10
To find the maximum speed during those minutes, we need to determine the highest value of the velocity function v=960t-5t.
First, we need to understand that the velocity function is a quadratic equation in the form of v = at^2 + bt + c, where a, b, and c are constants.
In our case, a = -5, b = 960, and c = 0 (since it's not provided).
To find the maximum speed, we can use the vertex formula. The x-coordinate of the vertex of a quadratic function in the form of ax^2 + bx + c is given by x = -b/2a.
In our case, x = -b/2a = -960/(2*(-5)) = -960/(-10) = 96.
Now, substitute this x value back into the velocity function to find the corresponding maximum speed:
v = 960t - 5t
v = 960(96) - 5(96)
v = 92160 - 480
v = 91680 ft/min
Therefore, the maximum speed during those 10 minutes is 91680 ft/min.