The velocity of the particle as a function of time

In summary, the conversation discusses solving a problem involving acceleration, velocity, and position of a particle. The issue at hand is whether or not the expression should include a "^". The person is seeking help and mentions that they have attempted a solution but are unsure if it is correct.
  • #1
yesmale4
41
1
Homework Statement
The acceleration of the particle is given by a(t)=bt y + c e kt z.
It is known that at t=0 the velocity of the particle is by v(0)= d x + c/k z and its position is r(0)= c/k2 z.
b, c, d and k are constants.
Relevant Equations
v\left(t\right)=\int \:a\left(t\right)dt
sa.png

this is how i try to solve it:
mm.jpeg


can someone please help me with that because i don't know what I am doing worng here.
 

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  • #2
Isn't the problem that it should be
Code:
(c/k)*exp(k*t)
(without the ^)?
 
  • #3
DrClaude said:
Isn't the problem that it should be
Code:
(c/k)*exp(k*t)
(without the ^)?
Thank you very much !
 
  • #4
yesmale4 said:
Homework Statement:: The acceleration of the particle is given by a(t)=bt y + c e kt z.
It is known that at t=0 the velocity of the particle is by v(0)= d x + c/k z and its position is r(0)= c/k2 z.
b, c, d and k are constants.
Relevant Equations:: v\left(t\right)=\int \:a\left(t\right)dt

View attachment 297864
this is how i try to solve it:
View attachment 297866

can someone please help me with that because i don't know what I am doing wrong here.
Is it telling you it is wrong or is that just what you think?
 

FAQ: The velocity of the particle as a function of time

What is the velocity of a particle as a function of time?

The velocity of a particle as a function of time is the rate of change of the particle's position with respect to time. It is a vector quantity that includes both the magnitude and direction of the particle's motion.

How is the velocity of a particle calculated?

The velocity of a particle can be calculated by taking the derivative of the particle's position function with respect to time. This means finding the rate of change of the position function over a small interval of time, which is represented by the symbol "d" in calculus.

What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they have different meanings in physics. Velocity is a vector quantity that includes both magnitude and direction, while speed is a scalar quantity that only includes magnitude. In other words, velocity tells us not only how fast an object is moving, but also in what direction.

How does the velocity of a particle change over time?

The velocity of a particle can change over time due to various factors such as acceleration, friction, and external forces. If there is no net force acting on the particle, its velocity will remain constant (constant velocity). However, if there is a net force, the velocity will change in the direction of the force (acceleration).

Can the velocity of a particle be negative?

Yes, the velocity of a particle can be negative. This indicates that the particle is moving in the opposite direction of the positive direction, which is typically defined as the direction of motion. For example, if a particle is moving to the left, its velocity would be negative since it is moving in the opposite direction of the positive x-axis.

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