Fewpal
0 votes
186 views
in Physics by (58.6k points)

A particle of mass 1kg moves in a straight line under the influence of a force, which increases linearly with the time at the rate of 60N per sec. At time t = 0 the initial force may be taken as 50N. Determine the acceleration and velocity of the particle 4sec after it started from rest at the origin.

1 Answer

+1 vote
by (66.3k points)
selected by
 
Best answer

As the force varies linearly with time, 

F = mt + C 

Differentiate the equation with time

dF/dt = m = 60(given) 

i.e., m = 60 ...(i) 

Given that, at t = 0, F = 50N, 

50 = 60 X 0 + C 

C = 50 ...(ii) 

Now the equation becomes, 

F = 60t + 50 ...(iii) 

Since, F = ma, m = 1Kg 

F = ma = 1.a = 60t +50 

At t = 4 sec, 

a = 60 X 4 + 50 = 290

also, a = dv/dt

a = dv/dt = 60t + 50

Integration both side for the interval of time 0 to 4sec

V = (60t2 + 50t), limit are 0 to 4

V = 30(4)2 + 50 X 4

V = 680m/sec

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...