What Are the Velocity and Acceleration of a Particle at t = 5.0 s?

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SUMMARY

The discussion focuses on calculating the velocity and acceleration of a particle at t = 5.0 s, based on a provided velocity-time graph. The particle starts from the origin and moves along the positive x-axis. Key calculations include the particle's coordinate at t = 5.0 s, which is derived from the graph, yielding a velocity of 2 m/s and an acceleration of 2 m/s². Average velocity and acceleration between t = 1.0 s and t = 5.0 s are also computed, confirming that the average acceleration is 0 m/s².

PREREQUISITES
  • Understanding of kinematic equations, specifically Vf = Vi + at
  • Familiarity with average velocity calculations, Vavg = (Vf + Vi) / 2
  • Knowledge of average acceleration concepts, a_avg = change in v / change in time
  • Ability to interpret velocity-time graphs
NEXT STEPS
  • Study the derivation and application of kinematic equations in one-dimensional motion
  • Learn how to analyze velocity-time graphs for various motion scenarios
  • Explore the relationship between displacement, velocity, and acceleration in physics
  • Investigate the implications of constant versus variable acceleration on particle motion
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Students studying physics, particularly those focusing on kinematics, as well as educators seeking to clarify concepts related to motion and graph interpretation.

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A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in Fig. 2-43;

144302b2-a5d9-4a80-a60b-3143ed308917.png


the v-axis scale is set by vs = 7.00 m/s. (a) What is the coordinate of the particle at t = 5.0 s? (b) What is the velocity of the particle at t = 5.0 s? (c) What is the acceleration of the particle at t = 5.0 s? (d) What is the average velocity of the particle between t = 1.0 s and t = 5.0 s? (e) What is the average acceleration of the particle between t = 1.0 s and t = 5.0 s?

Homework Equations


Vf= Vi+at
Vavg = (Vf+Vi)/2
a avg= change in v/change in time


The Attempt at a Solution



I think all my answers are wrong!
a) (2,5) --> Looking at the graph

b) t =5s, v=2 m/s

c) Vf= Vi+at
(4-2)/1 = a
a = 2 m/s

d) Vavg = (Vf+Vi)/2
(2=2)/2
= 2 m/s

e) a avg= change in v/change in time
=0 m/s
 
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you cannot calculate the coordinate by just looking at the graph. You have to use x=at^2/2
for b.) its just v_s/2 from the graph

c, how much the velocity decrease from t=4 to t=5? i.e. in one second?

d.) the formula is right but u read it wrong from the graph.

e,) correct.
 
for A, x=at^2/2
how do I find a??

Thanks though :D
 

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