Question

The position of an object of
mass 5 kg as a function of
time is giving by r = (20m/s4)t4
i + (12 m/s3)t3 j. Find the
force acting on the object as a
function of time. Express the
force in unit vectors. Hint:
Remember that Newton's
second Law relates the force
to the acceleration

Answer 1

Answer:

$F=5(240t^2i+72tj)\ N$

Explanation:

Given that,

The mass of the object, m = 5 kg

The position vector is, $r=20t^4i+12t^3j$

Velocity, $v=\dfrac{dr}{dt}=80t^3i+36t^2j$

Acceleration, $a=\dfrac{dv}{dt}=240t^2i+72tj$

Newton's second law of motion is given as follows:

F = ma

Put all the values,

$F=5(240t^2i+72tj)\ N$

Hence, this is the required solution.