Two particles are currently in motion along parallel, straight paths in the positive x-direction, between two timing gates that are spaced at a distance d from each other. They both pass the first timing gate with a “flying start”, at t0 = 0, and they move as follows: - Particle A is moving with a constant velocity, vA - Particle B passes the first timing gate with a momentary velocity vB0 > 0, and a constant acceleration of aB = const. - After some time t1, both particles meet again at the second timing gate! a) Write the motion path equations x(t) for each particle in algebraic form Solve the following questions numerically for these parameters: d = 600m, t1 = 100s, vB0 = 15m/s b) What is the constant velocity for particle A? c) What is the constant acceleration for particle B? d) At what time does particle B come to a stop? e) What is the velocity for particle B at the second gate at the time t1? f) What is the total distance travelled for particle B? g) What is the average speed for particle B during that time? What is its average velocity? h) Sketch the s(t) and v(t) motion diagrams for both particles, to scale i) Explain / interpret your results
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.
Two particles are currently in motion along parallel, straight paths in the positive x-direction, between two timing gates that are spaced at a distance d from each other. They both pass the first timing gate with a “flying start”, at t0 = 0, and they move as follows:
- Particle A is moving with a constant velocity, vA
- Particle B passes the first timing gate with a momentary velocity vB0 > 0, and a constant acceleration of aB = const.
- After some time t1, both particles meet again at the second timing gate!
a) Write the motion path equations x(t) for each particle in algebraic form
Solve the following questions numerically for these parameters: d = 600m, t1 = 100s, vB0 = 15m/s
b) What is the constant velocity for particle A?
c) What is the constant acceleration for particle B?
d) At what time does particle B come to a stop?
e) What is the velocity for particle B at the second gate at the time t1?
f) What is the total distance travelled for particle B?
g) What is the average speed for particle B during that time? What is its average velocity?
h) Sketch the s(t) and v(t) motion diagrams for both particles, to scale
i) Explain / interpret your results
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