A motorist drives along a straight road at a constant speed of 15.0 m / s . Just as she passes a

step 1 In this problem, we have to find in part A, that time it takes the police officer to reach the m

A motorist drives along a straight road at a constant speed...

A motorist drives along a straight road at a constant speed of $15.0 \mathrm{m} / \mathrm{s} .$ Just as she passes a parked motorcycle police officer, the officer starts to accelerate at $2.00 \mathrm{m} / \mathrm{s}^{2}$ to overtake her. Assuming the officer maintains this acceleration, (a) determine the time it takes the police officer to reach the motorist. Find (b) the speed and (c) the total displacement of the officer as he overtakes the motorist.

A motorist drives along a straight road at a constant speed of $15.0 \mathrm{m} / \mathrm{s} .$ Just as she passes a parked motorcycle police officer, the officer starts to accelerate at $2.00 \mathrm{m} / \mathrm{s}^{2}$ to overtake her. Assuming the officer maintains this acceleration,
(a) determine the time it takes the police officer to reach the motorist. Find (b) the speed and (c) the total displacement of the officer as he overtakes the motorist.

Key Concepts

Quadratic Equations in Kinematics

Kinematic problems that involve equating displacement expressions, particularly when one or more objects are accelerating, often lead to quadratic equations in time. Solving these quadratic equations yields important time intervals, such as the moment when one object catches up to another. Mastery of solving quadratic equations is therefore crucial in handling motion problems where multiple factors of time, velocity, and acceleration interplay.

Relative Motion

Relative motion involves examining the movement and positions of two or more objects with respect to one another. In problems where one object overtakes another, the positions of both objects are compared over time, and their displacement equations are set equal to find the exact moment of overtaking. This concept allows for the analysis of interactions between different types of motion, such as constant velocity versus acceleration.

Uniform Motion

Uniform motion refers to an object's movement at a constant speed in a straight line, where the displacement is directly proportional to time (displacement = speed × time). This concept is essential for analyzing situations where there is no acceleration and helps determine positions over time under constant speed conditions.

Uniformly Accelerated Motion

Uniformly accelerated motion deals with scenarios in which an object's acceleration remains constant. The motion can be described by kinematic equations such as displacement = initial velocity × time + 0.5 × acceleration × time² and velocity = initial velocity + acceleration × time. These equations are fundamental in calculating displacement, time, and final velocity when acceleration is present.

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