A mass of 1 kg is acted upon by a single force overset arrow F=(.4 hati+4 hatj.) N . Due to force, mass is displaced from (.0,0.) to (1 m , 1 m) . If initially, the speed of the particle was 2 m s- 1 , its final speed should approximately be

Question

A mass of 1 kg is acted upon by a single force overset arrow F=(.4 hati+4 hatj.) N . Due to force, mass is displaced from (.0,0.) to (1 m , 1 m) . If initially, the speed of the particle was 2 m s- 1 , its final speed should approximately be (A) 6 m s- 1 (B) 4.5 m s- 1 (C) 8 m s- 1 (D) 7.2 m s- 1

Tardigrade Admin · Accepted Answer

Mass is displaced from (0, 0) to (1, 1). Therefore displacement is,

S \to = (1 - 0) \hat{i} + (1 - 0) \hat{j}

S \to = (\hat{i} + \hat{j}) m

Given force

F \to = (4 \hat{i} + 4 \hat{j}) N

∴

Work done by a constant force,

W = F \to . S \to

W = (4 \hat{i} + 4 \hat{j}) . (\hat{i} + \hat{j})

W = 4 + 4 = 8 J

From work-energy theorem

Δ K = W

\frac{1}{2} m (ν_{2}^{2} - ν_{1}^{2}) = W

\frac{1}{2} (1) (ν_{2}^{2} - 2^{2}) = 8

ν_{2}^{2} = 20

ν_{2} = 4.5 m s^{- 1}

Q. A mass of $1 k g$ is acted upon by a single force $F \to = (4 \hat{i} + 4 \hat{j}) N$ . Due to force, mass is displaced from $(0, 0)$ to $(1 m, 1 m)$ . If initially, the speed of the particle was $2 m s^{- 1}$ , its final speed should approximately be

$6 m s^{- 1}$

$4.5 m s^{- 1}$

$8 m s^{- 1}$

$7.2 m s^{- 1}$

Q. A mass of 1kg is acted upon by a single force F→=(4i^+4j^​)N . Due to force, mass is displaced from (0,0) to (1m,1m) . If initially, the speed of the particle was 2ms−1 , its final speed should approximately be

6ms−1

4.5ms−1

8ms−1

7.2ms−1

Q. A mass of $1 k g$ is acted upon by a single force $F \to = (4 \hat{i} + 4 \hat{j}) N$ . Due to force, mass is displaced from $(0, 0)$ to $(1 m, 1 m)$ . If initially, the speed of the particle was $2 m s^{- 1}$ , its final speed should approximately be

$6 m s^{- 1}$

$4.5 m s^{- 1}$

$8 m s^{- 1}$

$7.2 m s^{- 1}$