Question

A particle of mass 2kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is 

(A) 10 ms^–1 

(B) 20 ms^–1 

(C) 75 ms^–1 

(D) 50 ms^–1

Answer 1

Correct option: (D) 50ms^–1

Explanation:

m = 2 kg

V_o = o m/s

velocity after 10 sec = V = (1 / 2) (area enclosed between F – t graph)

as F × t = m × a × t

F × t = m × v           a = (v / t)

v = {(F × t) / m}

v = (1 / 2) (area under F – t curve)

= (1 / 2) × [{(1 / 2) × 2 × 10} + (2 × 10) + {(1 / 2) × 2(10 + 20)} + {(1 / 2) × 4 × 20}]

= (1 / 2) [10 + 20 + 30 + 40]

= 50 m/s