A particle starts at x = 0 and moves along the x-axis at velocity v(t) = 5 for time t ≥ 0. Where is the particle at t = 4?

Question

A particle starts at x = 0  and moves along the x-axis at velocity v(t) = 5 for time t ≥ 0. Where is the particle at t = 4?

agent47 · Answer

draw isn't working....

agent47 · Answer

v(t) = 5
Distance is the integral of velocity from 0 to 5.

perl · Answer

position is the integral of velocity,  so  x(t) = 5*t + c  , and since x(0) = 0, we have
x(0) = 5*0 + c , c = 0.

so x(t) = 5t , and at t= 4  
x(4) = 5*4 = 20 units

agent47 · Answer

And you don't have to worry about splitting it up as it's in one direction only.

perl · Answer

20 units in the positive direction (where you defined positive as right or left)

shamil98 · Answer

so basically you integrate the equation v(t) = 5 and do what you did for questions like these?

perl · Answer

yes