Question

The position of an object moving in xy plane is
described by r = (ti + 2tſ) m. Velocity of object at
time t = 1 s, is
(1) 13 ms
(2) V5 ms
(3) 3 ms-1
(4) 5 ms*
oloit​

Answer 1

The position of an object moving in xy plane is described by r = (ti + 2t j) m. Velocity of object at time t = 1 s, is

answer : √5 m/s

explanation : The position of an object moving in xy plane is described by r = (t i + 2t j) m

we know, velocity is the rate of change of displacement (or position) with respect to time. i.e., v = dr/dt

so, differentiating r with respect to time t to get velocity.

so, v = dr/dt = d(t i + 2t j)/dt

= (dt/dt) i + 2(dt/dt) j

=( i + 2 j ) m/s

velocity is constant for all value of t.and that is v = (i + 2j) m/s

so, magnitude of velocity = √(1² + 2²) = √5 m/s