A point moves along the x-axis, and its x-coordinate after t sec is x = 4t + 16. (Assume that x is in centimeters.)
(a) What is the velocity? in cm/sec
To find the velocity of the point, we need to differentiate the equation x = 4t + 16 with respect to time (t). The derivative of x with respect to t will give us the velocity.
Given that x = 4t + 16, let's find the derivative of x with respect to t:
dx/dt = d/dt (4t + 16)
= d/dt (4t) + d/dt (16)
= 4 + 0 (since derivative of a constant is zero)
= 4
Therefore, the velocity of the point is 4 cm/sec.