Question

14. A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. It
starts its journey from rest at x = 0, then its velocity at x = 12 m is:
1) 0
2) 20√2 m/s
3) 40 m/s
4) 20√3 m/s
​

Answer 1

Answer:

3) 40 m/s ............

Answer 2

Answer:

Explanation:

v = 40m/s,

Given:

m = 0.1 kg,

Solution:  

Area under the graph can be computed by,

IMAGE,

m = 0.1 kg  ,

For area (0-4) = ½ (upper limit – lower limit) × F(N) = ½ (4-0) × (10) = 20,

For area (4-8) = ½ (upper limit – lower limit) x F(N) = (8-4) x (10) = 40,

For area (8-12) = ½ (upper limit – lower limit) × F(N) = ½ (12-8) × (10) = 20,

Total area = 20+40+20 = 80,

To find velocity =1/2 m × v²,

1/2 m × v²=80,

(0.1) x v²=160,

v²= 160/0.1 = 1600 ,

v = √1600 = 40m/s.

So,option 3 : 40 m/s is the correct answer.

Hope it helps.