A man drives a car at v1= 54mi/h and suddenly notices a truck at a distance d= 13.5 m in front of him. That truck is moving in the same direction at a constant velocity v2= 34 mi/h. In order to not collide the person in the car must reduce their speed to v2 in a time interval, by slamming the brakes. the driver can give the car a maximum acceleration of ax. assume the acceleration is constant and the motion is in the positive direction. so that ax<0. 1) if the driver just barely avoids collision what is the final distance between the car and the truck? 2) write an expression for the distance Δx2 traveled by the truck in the time Δt, in terms of the quantities defined in the problem. 3) write an expression for the distance Δx1 traveled by the car in the time Δt, assuming the driver brakes as hard as they can. 4)Relate the total distance the car travels Δx1 to the distance the truck travels and the initial distance between them. 5)Find the acceleration of the car in terms of its initial velocity,v1, its final velocity, v2, and the time interval Δt. 6 Use your results from (2) through (5) to find a symbolic expression for the time Δt in terms of v1, v2 and d. 7).Calculate the numerical value of Δt in seconds. 8). Using your result from (6), find a symbolic expression for the acceleration ax. 9)Calculate the value of ax, in meters per second squared.
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.
A man drives a car at v1= 54mi/h and suddenly notices a truck at a distance d= 13.5 m in front of him. That truck is moving in the same direction at a constant velocity v2= 34 mi/h. In order to not collide the person in the car must reduce their speed to v2 in a time interval, by slamming the brakes. the driver can give the car a maximum acceleration of ax. assume the acceleration is constant and the motion is in the positive direction. so that ax<0.
1) if the driver just barely avoids collision what is the final distance between the car and the truck?
2) write an expression for the distance Δx2 traveled by the truck in the time Δt, in terms of the quantities defined in the problem.
3) write an expression for the distance Δx1 traveled by the car in the time Δt, assuming the driver brakes as hard as they can.
4)Relate the total distance the car travels Δx1 to the distance the truck travels and the initial distance between them.
5)Find the acceleration of the car in terms of its initial velocity,v1, its final velocity, v2, and the time interval Δt.
6 Use your results from (2) through (5) to find a symbolic expression for the time Δt in terms of v1, v2 and d.
7).Calculate the numerical value of Δt in seconds.
8). Using your result from (6), find a symbolic expression for the acceleration ax.
9)Calculate the value of ax, in meters per second squared.
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