During a test by the editors of an auto magazine, the...

During a test by the editors of an auto magazine, the distance $s$ (in feet) traveled by the MacPherson $X$ - 2 racing car $t$ sec after the brakes were applied conformed to the rule $$ s=f(t)=120 t-15 t^{2} \quad(t \geq 0) $$ a. Find an expression for the car's velocity $v$ at any time $t$ b. What was the car's velocity when the brakes were first applied? c. What was the car's stopping distance for that particular test? Hint: The stopping time is found by setting $v=0$

During a test by the editors of an auto magazine, the distance $s$ (in feet) traveled by the MacPherson $X$ - 2 racing car $t$ sec after the brakes were applied conformed to the rule
$$
s=f(t)=120 t-15 t^{2} \quad(t \geq 0)
$$
a. Find an expression for the car's velocity $v$ at any time $t$
b. What was the car's velocity when the brakes were first applied?
c. What was the car's stopping distance for that particular test?
Hint: The stopping time is found by setting $v=0$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solving for Stopping Conditions

Calculating stopping distance involves determining when the object’s velocity becomes zero, which indicates that the object has come to a stop. This usually entails solving equations derived from the velocity function and then substituting the stopping time into the position function to find the total distance traveled.

Differentiation

Differentiation is the mathematical process used to calculate the derivative of a function, expressing how one quantity changes in relation to another. In kinematics, differentiating the distance (or position) function with respect to time provides the velocity function, which describes the object's instantaneous rate of change of position.

Velocity as the Derivative of Position

In physics, velocity is defined as the derivative of the position function with respect to time. This relationship allows us to determine how quickly an object is moving and in what direction at any given moment, which is essential for analyzing motion.

Kinematics and Motion Analysis

Kinematics is a branch of mechanics that deals with describing the motion of objects without considering the causes of motion. It involves analyzing variables such as displacement, velocity, acceleration, and time to describe movement, especially under conditions of constant acceleration.

Transcript

Please give Ace some feedback