Driving to Red Hook at night at 65 miles/hour, a Bard student sees a deer in the road 50 meters straight ahead, frozen in the car headlights. The student immediately slams on the breaks, decelerating (negatively accelerating) the car at a constant 8 m/s2. If the deer remains frozen in place, does the student avoid hitting the deer?
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.
given initial speed u=65 mi/h = 0.447 * 65 =29.055 m/s
acceleration a =-8 m/s
distance between bear and car . s = 50 m
using equation of motion v2=u2 + 2as
where v is the final speed
substituting values
v2=29.0552 - 2*8*50 =44.193
therefore final speed v =(44.193)1/2 =6.65 m/s
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