Question

The position vector of an object of mass 0.5 kg is given by r 2.0t2i+ 3.0tj m where t represents time. Which ONE of the following statements is FALSE when a time of t 2.0 s has elapsed. a) The object has moved a distance of 10 m. b) The momentum of the object is 41+1.5/ kg.m.s c) The kinetic energy of the object is 18 J d) The force on the object acts perpendicular to the direction of the unit vectorj e) The magnitude of the force acting on the object is 4 N

Answer 1

Answer:

All statements but (a) and (d) are FALSE

Explanation:

To know the distance, the object has moved, we evaluate the position at t=2 and then calculate its module:

r(2) = 8i + 6j    Therefore: D = 10m  (Statement (a) is true)

The momentum is given by:

P(2) = m*V(2)   We need to derive position to get the velocity:

V(t) = 4t i  +  3 j   At t=2s:   V(2)=8i + 3j m/s

So, the momentum is:

P(2) = 4i + 1.5j kg.m/s   Hence, part (b) is false (or there's an error on the question)

Kinetic energy:

$Ek = m*V(2)^2/2 = 18.25J$   It's almost equal to part (c) but not close enough.

The net force will be in the same direction as the acceleration, so we have to derive velocity:

a(t) = 4 i m/s^2     It IS perpendicular to unit vector j, (Statement (d) is true)

The magnitude of the net force will be:

F = m*a(2) = 2N    Not 4N, therefore, part (e) is False