A body moving with constant acceleration in a straight line crosses two points A and B with a speed of 2m/s and 14m/s respectively. The speed of the object at the midpoint of A and B are
Answers
Explanation:
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Answer:
The speed of the object at the midpoint of A and B is 10 m/s.
Explanation:
Given :
A body moving with constant acceleration in a straight line crosses two points A and B with a speed of 2m/s and 14m/s respectively.
To find :
the speed of the object at the midpoint of A and B
Solution :
Let
- the total distance (AB) = 2x
- acceleration = a
- speed at the midpoint = v m/s
- Speed at A = 2 m/s
- Speed at B = 14 m/s
Using third equation of motion : v² - u² = 2as
From A to midpoint :
distance = x
acceleration = a
initial speed, u = 2 m/s
final speed = v
Substituting,
v² - 2² = 2(a)(x)
v² - 4 = 2ax --[1]
From midpoint to B :
distance = x
acceleration = a
initial speed, u = v m/s
final speed, v = 14 m/s
Substituting,
14² - v² = 2(a)(x)
196 - v² = 2ax --[2]
From [1] and [2],
v² - 4 = 196 - v²
v² + v² = 196 + 4
2v² = 200
v² = 200/2
v² = 100
v = √100
v = 10 m/s
∴ The speed of the object at the midpoint of A and B is 10 m/s.