Learning Goal: To practice Problem-Solving Strategy 2.1 for constant acceleration problems. A car is traveling at a constant velocity of magnitude v0v0 when the driver notices a garbage can on the road in front of him. At that moment, the distance between the garbage can and the front of the car is ddd. A time treacttreact after noticing the garbage can, the driver applies the brakes and slows down at a constant rate before coming to a halt just before the garbage can. What is the magnitude of the car's acceleration after the brakes are applied? PROBLEM-SOLVING STRATEGY 2.1 Kinematics with constant acceleration MODEL: Model the object as having constant acceleration. VISUALIZE: Use different representations of the information in the problem. Draw a pictorial representation. This helps you assess the information you are given and starts the process of translating the problem into symbols. Use a graphical representation if it is appropriate for the problem. Go back and forth between these two representations as needed. SOLVE: The mathematical representation is based on the three kinematic equations vfs=vis+asΔtvfs=vis+asΔt, sf=si+visΔt+12as(Δt)2sf=si+visΔt+12as(Δt)2, and v2fs=v2is+2asΔsvfs2=vis2+2asΔs. Use xxx or yyy, as appropriate to the problem, rather than the generic sss. Replace ii and ff with numerical subscripts defined in the pictorial representation. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Part A Below is a sketch of the situation described in this problem, along with four different motion diagrams. Which of these diagrams is the correct pictorial representation of the problem?
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.
Learning Goal:
PROBLEM-SOLVING STRATEGY 2.1
MODEL: Model the object as having constant acceleration.
VISUALIZE: Use different representations of the information in the problem.
- Draw a pictorial representation. This helps you assess the information you are given and starts the process of translating the problem into symbols.
- Use a graphical representation if it is appropriate for the problem.
- Go back and forth between these two representations as needed.
SOLVE: The mathematical representation is based on the three kinematic equations
vfs=vis+asΔtvfs=vis+asΔt,
sf=si+visΔt+12as(Δt)2sf=si+visΔt+12as(Δt)2, and
v2fs=v2is+2asΔsvfs2=vis2+2asΔs.
- Use xxx or yyy, as appropriate to the problem, rather than the generic sss.
- Replace ii and ff with numerical subscripts defined in the pictorial representation.
REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question.
Part A
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