Object A has a position as a function of time given by _A(t) = (3.00 m/s) t
+ (1.00 m/s²) t²

) Object B has a position as a function of time given by
_B(t) = (4.00 m/s) t
+ (-1.00 m/s²) t²

) All quantities are SI units.What is the distance between object A and object B at time t = 3.00 s?

Question

Object A has a position as a function of time given by

_A(t) = (3.00 m/s) t

+ (1.00 m/s²) t²

) Object B has a position as a function of time given by

_B(t) = (4.00 m/s) t

+ (-1.00 m/s²) t²

) All quantities are SI units.What is the distance between object A and object B at time t = 3.00 s?

Quizplus · Accepted Answer

The distance between objects A and B at time t is given by the expression:

11ea8401_fc19_6285_aeff_b5a5a665808c_TB6682_11

To find the distance at t = 3 s, we substitute t = 3 s into this expression and simplify:

11ea8401_fc19_6285_aeff_b5a5a665808c_TB6682_11

= sqrt((3.00 m/s - 4.00 m/s)^2 + (1.00 m/s - (-1.00 m/s))^2) * 3 s 
= sqrt((-1.00 m/s)^2 + (2.00 m/s)^2) * 3 s 
= sqrt(5) * 3 s 
= 15.0 m

Therefore, the distance between objects A and B at time t = 3.00 s is 15.0 m.

Object a Has a Position as a Function of Time