The position of an object changes with time according to the expression x(t) = 5t62 = 3t - 1. What is the position of the object when its velocity is 11 m/s?
To determine the position of the object when its velocity is 11 m/s, we need to find the time at which the object has a velocity of 11 m/s and then substitute that time into the position equation.
First, let's find the time when the velocity is equal to 11 m/s. Velocity is the derivative of position with respect to time, so we need to find the derivative of the position equation and set it equal to 11:
v(t) = dx(t)/dt = d/dt (5t^2 + 3t - 1) = 10t + 3
Now we set the velocity equation equal to 11 and solve for t:
10t + 3 = 11
10t = 11 - 3
10t = 8
t = 8/10
t = 0.8 seconds
Now that we have the time at which the velocity is 11 m/s (t = 0.8 seconds), we can substitute this value into the position equation to find the position of the object:
x(t) = 5t^2 + 3t - 1
x(0.8) = 5(0.8)^2 + 3(0.8) - 1
x(0.8) = 5(0.64) + 2.4 - 1
x(0.8) = 3.2 + 2.4 - 1
x(0.8) = 4.6 meters
Therefore, the position of the object when its velocity is 11 m/s is 4.6 meters.