Question

A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t) = αt² - βt³, where α = 1.45 m/s² and β = 0.0490 m/s³. Find the velocity v(t) of the car.

Answer 1

The velocity v(t) of the Honda Civic is found by taking the first derivative of the position function, resulting in v(t) = 2.9t - 0.147t². This represents the car's velocity as a function of time.

Step-by-step explanation:

The student is asking for the velocity v(t) of a Honda Civic whose position x as a function of time t is given by the equation x(t) = αt² - βt³, where α represents the initial acceleration and β is a third-degree term coefficient. To find the velocity, we need to take the first derivative of the position function with respect to time.

The position function is:

x(t) = 1.45t² - 0.0490t³

By taking the derivative, we get the velocity function:

v(t) = dx/dt = 2(1.45)t - 3(0.0490)t²

v(t) = 2.9t - 0.147t²

This equation represents the velocity of the car at any given time t.