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.

Explanation:

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 .

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

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