The position of a particle is given by the position vector, r (t) = (3t) i + (-4.9t2) j, where r is in meters and t is in seconds. a) What is its position at t = 2 s? b) What is the instantaneous velocity of the particle? c) What is the instantaneous velocity at t = 2 s? d) What is the acceleration of the particle? e) Sketch the position, velocity, and acceleration vectors at t = 2 s.

a)

r (t) = (3t) i + (-4.9t2) j

At t = 2

r (t) = (3 x 2) i + (-4.9 x 2²) j

= 6i - 19.6 j

magnitude = R

R² = 6² + 19.6²

R = 20.5 m/s

b)

r (t) = (3t) i + (-4.9t2) j

velocity

= dr/dt = 3 i - 9.8 t j

c)

At t = 2

instantaneous velocity

= 3 i - 9.8 t j

at t = 2

= 3i - 9,8 x 2j

= 3i - 19.6 j

magnitude

= 19.82 m/s

d)

acceleration a

dr/dt = 3 i - 9.8 t j

Again differentiating

d²r/dt² = - 9.8 j

acceleration = 9.8 m / s² towards - ve y axis.