A car is approaching a hill at 30.0 m / s when its engine suddenly fails just at the bottom of t

step 1 Hello everyone here it is given a car is approaching a hill at speed of 30 meter per second so i

A car is approaching a hill at 30.0 m / s when its engine...

A car is approaching a hill at $30.0 \mathrm{m} / \mathrm{s}$ when its engine suddenly fails just at the bottom of the hill. The car moves with a constant acceleration of $-2.00 \mathrm{m} / \mathrm{s}^{2}$ while coasting up the hill. (a) Write equations for the position along the slope and for the velocity as functions of time, taking $x=0$ at the bottom of the hill, where $v_{i}=30.0 \mathrm{m} / \mathrm{s} .$ (b) Determine the maximum distance the car rolls up the hill.

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Key Concepts

Kinematics Equations for Constant Acceleration

This concept involves using the standard equations of motion to describe the position and velocity of an object undergoing constant acceleration. The position function typically takes the form x(t) = x? + v?t + (1/2)at², while the velocity function is given by v(t) = v? + at. These equations allow one to predict the future state of the moving object, and they are fundamental to understanding linear motion in physics.

Determining Maximum Displacement Using Boundary Conditions

When an object moves up an incline under constant deceleration, the maximum distance is reached when its velocity becomes zero. Setting the velocity equation to zero allows one to solve for the time at which the object stops momentarily. This time value can then be substituted back into the position equation to determine the maximum displacement. This process is a key technique in kinematics used to analyze motion where an object comes to a halt under uniform negative acceleration.

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