Answer:
a)[tex]a=5 i+2t j - 6\ t^2k[/tex]
b)[tex]a=\dfrac{1}{24.83}(5i+4j-24k)\ m/s^2[/tex]
Explanation:
Given that
v(t) = 5 t i + t² j - 2 t³ k
We know that acceleration a is given as
[tex]a=\dfrac{dv}{dt}[/tex]
[tex]\dfrac{dv}{dt}=5 i+2t j - 6\ t^2k[/tex]
[tex]a=5 i+2t j - 6\ t^2k[/tex]
Therefore the acceleration function a will be
[tex]a=5 i+2t j - 6\ t^2k[/tex]
The acceleration at t = 2 s
a= 5 i + 2 x 2 j - 6 x 2² k m/s²
a=5 i + 4 j -24 k m/s²
The magnitude of the acceleration will be
[tex]a=\sqrt{5^2+4^2+24^2}\ m/s^2[/tex]
a= 24.83 m/s²
The direction of the acceleration a is given as
[tex]a=\dfrac{1}{24.83}(5i+4j-24k)\ m/s^2[/tex]
a)[tex]a=5 i+2t j - 6\ t^2k[/tex]
b)[tex]a=\dfrac{1}{24.83}(5i+4j-24k)\ m/s^2[/tex]
