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