two cars A and B cross a point P with velocity 10 metre per second and 15 M per second after that they move with different uniform acceleration and the car A overtakes B with speed 25m per second what is the velocity of B at that instant
Answers
Velocity refers to "the rate at which an object changes its position per unit time". It is a vector quantity which depends on magnitude and direction.
Velocity of B = V of B - Velocity of A
25 = V of B - 10
Hence, velocity of B = 25+ 10
Velocity of B = 35 m\sec
Hence the relative velocity will be
35 - 15 = 20 m\sec
Relative velocity = 20 m\sec
Answer:
Explanation:
Given :-
Initial velocity of car A, u₁ = 10 m/s
Initial velocity of car B, u₂ = 15 m/s
Final velocity of car A, v₁ = 25 m/s
To Find :-
Final velocity of car B, v₁ = ??
Formula to be used :-
1st and 2nd equation of motion,
v = u + at and s = ut + 1/2 at²
Solution :-
Putting all the values, we get
v = u + at
⇒ v₁ = u₁ + a₁ × t
⇒ a₁ × t = v₁ - u₁
⇒ a₁ × t = 25 - 10
⇒ a₁ × t = 15 ..... (i)
Now, v = u + at
⇒ a₂ × t = u₂ - v₂
⇒ a₂ t + 15 = v₂ .... (ii)
Now, s = ut + 1/2 at²
Comparing both sides, we get
⇒ s = ut + 1/2 at² = s = ut + 1/2 at²
⇒ u₁ × t + 1/2 × a₁ × t² = u² × t + 1/2 × a₂ × t²
⇒ u₁ + 1/2 × a₁ × t = u₂ + 1/2 × a₂ × t
⇒ 10 - 15 = 1/2 (At - at)
⇒ - 5 × 2 = a₂t - a₁ t
⇒ - 10 = a₂t - a₁t
⇒ a₂t = a₁t - 10
⇒ a₂t = 15 - 10 [From Eq (i)]
⇒ a₂t = 5 m/s
⇒ 5 + 15 = v₂ [ From (ii)]
⇒ v² = 20 m/s
Hence, the velocity of B at that instant is 20 m/s.