At the instant the traffic light turns green, an automobile...

At the instant the traffic light turns green, an automobile starts with a constant acceleration $a$ of $2.2 \mathrm{~m} / \mathrm{s}^{2}$. At the same instant a truck, traveling with a constant speed of $9.5 \mathrm{~m} / \mathrm{s}$, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

Key Concepts

Kinematic Equations

Kinematic equations are fundamental tools in physics that relate the variables of motion—displacement, initial velocity, final velocity, acceleration, and time. These equations are applied to analyze and solve problems in both uniformly accelerated motion and uniform motion by eliminating the need for calculus in many cases.

Relative Motion

Relative motion involves comparing the motions of two or more objects from a common frame of reference. In problems where one object starts from rest and accelerates while another moves at a constant speed, analyzing when and where their displacements become equal allows one to determine the point of overtaking or intersection.

Constant Acceleration

This concept refers to an object’s motion when its velocity changes at a constant rate over time. It implies that the object experiences a uniform change in speed per unit time, which can be modeled using kinematic equations. Such equations allow one to calculate quantities like displacement, time, and final velocity when the initial velocity and acceleration are known.

Uniform Velocity

Uniform velocity describes motion where the object moves at a constant speed in a straight line, meaning there is no acceleration. In scenarios involving uniform velocity, the displacement is proportional to the time elapsed, making the computation of distance straightforward as it is simply the product of constant speed and time.

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