Question

A mass of 1 kg is acted upon by a single force F =(4î+4j) N. Due to this force, the mass is displaced from (0, 0) to (1m, 1m). If initially the speed of the particle was 2 ms^-1. Its speed should be
(approximately)
(A) 6 ms^-1
(B) 4.5 ms^-1
(C) 8 ms^-1
(D) 7.2 ms^-1​

Answer 1

answer : option (B) 4.5 m/s

force acting on particle , F = (4i + 4j) N

due to force mass is displaced from (0,0) to (1,1).

so, ∆x = (1 - 0)i + (1 - 0)j = 1i + 1j

so, workdone due to force , W = F.∆x

= (4i + 4j).(1i + 1j )

= 4 + 4 = 8j

now from conservation of work energy theorem,

workdone = change in kinetic energy

⇒ 8J = 1/2 m(v² - u²)

⇒8 = 1/2 × 1 (v² - 2²)

⇒16 = v² - 4

⇒v² = 20

⇒v = 2√5 = 4.472 ≈ 4.5 m/s

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Answer 2

$\huge\bold\purple{Answer:-}$

(B) 4.5 ms^-1