A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, friction-less surface of an ice covered lake. Then a force directed east and with magnitude F (t) = (16.8 N/s) t is applied. How far does the object travel in the first 5.00 s after the force is applied?

s = 23.34 m

Explanation:

given,

F = 16.8 t

mass = 45 Kg

time = 5 s

distance traveled by the object = ?

now,

Force acting at time 5 s

F = 16.8 x 5

F = 84 N

we know,

F = ma

84 = 45 x a

a = 1.867 m/s²

initial velocity = 0 m/s

using equation of motion for velocity calculation

v = u + at

v = 0 + 1.867 x 5

v = 9.335 m/s

again using equation of motion for distance calculation

v² = u² + 2 a s

9.335² = 0 + 2 x 1.867 x s

s = 23.34 m

distance traveled is equal to 23.34 m.