Vector Acceleration: Is 1/2at Equivalent?

[batballbat]

What is the equivalent vector of an acceleration a in terms of vector. Isnt it 1/2 at? In my book it is at

 

[grzz]

If the poster can be more clear about what is his difficulty one can give some help.

 

[batballbat]

there is an acceleration vector. What will be the velocity vector for that motion for time t?

 

[grzz]

Given a vector for acceleration at time t one can find the vector for the velocity at the same time t by integrating with respect to t the vector for acceleration.

 

[grzz]

e.g

if \underline{a} = 4t\underline{i} + t^{2}\underline{j}

then \underline{v} = 2t^{2}\underline{i}+ \frac{t^{3}}{3}\underline{j} + some constant vector.

 

[batballbat]

suppose a force is acting on a point with acceleration a. What would be the velocity vector for the same effect?

 

[grzz]

\underline{v} = \int\underline{a}dt

but \underline{F} = m\underline{a}

therefore

\underline{v} = \int\frac{\underline{F}}{m}dt