The velocity of the particle as a function of time

[yesmale4]

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

this is how i try to solve it:

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

 

[DrClaude]

Isn't the problem that it should be

(c/k)*exp(k*t)

(without the ^)?

 

[yesmale4]

Isn't the problem that it should be

(c/k)*exp(k*t)

(without the ^)?

Thank you very much !

 

[bob012345]

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?