Velocity Acceleration and Displacement

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SUMMARY

The discussion focuses on deriving expressions for velocity and acceleration from the displacement equation x = A + Bt³, where A = 3.5 m and B = 2.5 m/s³. The user seeks to calculate displacement, velocity, and acceleration at t = 2.0 s. The velocity is found by differentiating the displacement function with respect to time, resulting in v(t) = d(x)/dt = 3Bt², and acceleration is derived as a(t) = d(v)/dt = 6Bt. The user is encouraged to visualize these relationships through sketches of the velocity and acceleration graphs over time.

PREREQUISITES
  • Understanding of basic calculus, specifically differentiation.
  • Familiarity with kinematic equations in physics.
  • Knowledge of the concepts of velocity and acceleration as derivatives of displacement.
  • Basic graphing skills to visualize functions over time.
NEXT STEPS
  • Study the principles of kinematics, focusing on displacement, velocity, and acceleration relationships.
  • Learn how to differentiate polynomial functions to derive velocity and acceleration.
  • Explore graphical representations of motion, including velocity-time and acceleration-time graphs.
  • Review real-world applications of linear motion equations in physics problems.
USEFUL FOR

Physics students, educators, and anyone interested in understanding the fundamentals of linear motion and kinematics.

Shanice80
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Homework Statement



Hi am a physics beginner love it but seem to have issues with understanding Linear motion .. Anyway i have a question ..will be glad if could help .
" A car moves along a road in such a way that the distance x ,traveled in a time t ,is given by x=a+bt(to the power 3) where A and B have constant values of 3.5m and 2.5ms-3 respectively .
Derive expressions for the velocity and acceleration as a function of time and calculate the values of displacement ,velocity and acceleration at t=2.0s .
Then draw a rough sketch to show how the velocity and acceleration vary with time..
Thanks ...

Homework Equations





The Attempt at a Solution

 
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ok so you know that x=A+Bt3 and you are given A and B, now write down the equation of x with A and B with their respective values.


Shanice80 said:

Homework Equations




How do you find velocity when given displacement as a function of time? (i.e. what is the relation between velocity, displacement and time?

Similar for acceleration.


EDIT: Read up on http://en.wikipedia.org/wiki/Kinematics"
 
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