You are driving a car behind a truck. Both your car and the truck are moving at a speed of 80km/hr. If the driver of the truck suddenly slams on the brakes, what minimum distance between your car and the truck is needed so that your car does not crash into the truck’s rear end? (This is called the “minimum trailing distance”.) To simplify this problem, assume that the truck and the car have the same braking acceleration.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
You are driving a car behind a truck. Both your car and the truck are moving at a speed of 80km/hr. If the driver of the truck suddenly slams on the brakes, what minimum distance between your car and the truck is needed so that your car does not crash into the truck’s rear end? (This is called the “minimum trailing distance”.) To simplify this problem, assume that the truck and the car have the same braking acceleration.
A. In order to simplify the calculations for this problem, you are told to assume that the braking acceleration of the car and the truck are the same. What other reasonable assumptions do you need to make in order to solve this problem?
B. For both the truck and the car, draw an acceleration- and velocity-versus-time graph.
C. Find an expression for the minimum trailing distance. (Your expression should only contain symbols of physical quantities. No numbers are needed here. )
D. Find the numerical value for the minimum trailing distance (Plug the values of physical quantities into your expression from part A (do not forget units!))
E. Evaluate your answer that you found in part A by using limiting case analysis. In other words, consider what would happen to the minimum trailing distance if one of the variables in your expression from part A becomes very large or very small. At this extreme value, is the behavior of the minimum trailing distance expected and/or reasonable? If not, this may indicate that something is wrong with your expression.
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