The velocity and acceleration of particle give position vector

In summary, velocity is the rate of change of an object's position with respect to time, while acceleration is the rate of change of an object's velocity with respect to time. The velocity of a particle can be found by taking the derivative of its position vector with respect to time, and the formula for calculating acceleration is a = (vf - vi) / t. Average velocity is the total displacement of an object divided by the total time taken, while instantaneous velocity is the velocity of an object at a specific moment in time. The direction of acceleration for a particle is determined by the change in its velocity vector, with an increasing velocity resulting in an acceleration vector in the same direction and a decreasing velocity resulting in an acceleration vector in the opposite direction
  • #1
jake241190
2
0
the position vector of the particle is given by

s=e^-2ti+sin(2t)j+5t^k

calculate its velocity and acceleration at t=0
to get the velocity i differentiated with respect to t and substituted in t=0, giving me

velocity=-2i+2j and that's the same as the answer given but I am not sure how to get the acceleration i tried differentiating again and got a answer
acceleration= 4i+0i+0k and this isn't correct
 
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  • #2
never mind i know what I've don i forgot to differentite the k bit the second time giving
acceleration= 4i+10k
 

FAQ: The velocity and acceleration of particle give position vector

What is the difference between velocity and acceleration?

Velocity is the rate of change of an object's position with respect to time, while acceleration is the rate of change of an object's velocity with respect to time. In simpler terms, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how much an object's velocity is changing over time.

How is the velocity of a particle related to its position vector?

The velocity of a particle can be found by taking the derivative of its position vector with respect to time. In other words, the velocity is the instantaneous rate of change of the position vector.

What is the formula for calculating acceleration?

The formula for acceleration is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time interval. This formula applies to particles with constant acceleration.

What is the difference between average and instantaneous velocity?

Average velocity is the total displacement of an object divided by the total time taken, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity gives us an overall idea of how fast an object is moving, while instantaneous velocity tells us the exact speed and direction at a specific point in time.

How can we determine the direction of acceleration for a particle with a changing velocity?

The direction of acceleration for a particle is determined by the change in its velocity vector. If the velocity vector is increasing, the acceleration vector is in the same direction. If the velocity vector is decreasing, the acceleration vector is in the opposite direction. If the velocity vector is changing direction, the acceleration vector is perpendicular to the velocity vector.

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