Answer:
v = (6.77 j) m/s
s = (4.03 i + 5.46 j) m
Explanation:
Acceleration is given as:
a = -3.1 i + 4.2 j
Integrate to find velocity:
v = (-3.1 t + C₁) i + (4.2 t + C₂) j
Given that v(0) = 5.0 i:
C₁ = 5.0
C₂ = 0
v = (-3.1 t + 5.0) i + (4.2 t) j
Integrate again to find position:
s = (-1.55 t² + 5.0 t + C₃) i + (2.1 t² + C₄) j
Given that s(0) = 0 i + 0 j:
C₃ = 0
C₄ = 0
s = (-1.55 t² + 5.0 t) i + (2.1 t²) j
The maximum x coordinate occurs when the x component of the velocity is 0.
-3.1 t + 5.0 = 0
3.1 t = 5.0
t = 1.61
The velocity and position at this time are:
v = 6.77 j
s = 4.03 i + 5.46 j
