Aparticle of mass m=5.00 kilograms is at rest at t=0.00 seconds. a varying force f(t)=6.00t2−4.00t+3.00 is acting on the particle between t=0.00 seconds and t=5.00 seconds. find the speed v of the particle at t=5.00 seconds. express your answer in meters per second to three significant figures.

The speed v of the particle at t=5.00 seconds = 43 m/s

Explanation:

Given :

mass m = 5.00 kg

force f(t) = 6.00t2−4.00t+3.00 N

time t between t=0.00 seconds and t=5.00 seconds

From mathematical expression of Newton's second law;

Force = mass (m) x acceleration (a)

F = ma              

     ...... (1)

acceleration (a)   ......(2)

substituting (2) into (1)

Hence, F

Integrating both sides

The force is acting on the particle between t=0.00 seconds and t=5.00 seconds;

    ......(3)

Substituting the mass (m) =5.00 kg of the particle, equation of the varying force f(t)=6.00t2−4.00t+3.00 and calculating speed at t = 5.00seconds into (3):

v = 43 meters per second

The speed v of the particle at t=5.00 seconds = 43 m/s

answer: 31, 5556. 952 seconds