The velocity v of a particle moving along a straight linewhen at a distance x from the origin is given by a+ bv^2 = x^2 where a and b are constants. Then the acceleration is...
1. b/x
2. a/x
3. x/b
4. x/a
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Hello Friend,
→ Here, we have been given an equation relating velocity v and distance x from origin.
♦ Let acceleration be denoted by 'w'
(The letter 'a' is already used as constant. So I'm using a different letter here)
Thus, w = dv/dt (First derivative of velocity with respect to time)
Also, v = dx/dt
→ Now, given equation is:
a + b v² = x²
(Differentiating with respect to time)
So, d(a)/dt + d(bv²)/dt = d(x²)/dt
So, 0 + b (2v) dv/dt = 2x dx/dt
[a is constant. So da/dt = 0
Now, dv/dt = w, and dx/dt = v ]
So, 2bv w = 2x v
[v is common on both sides. So cancel it]
So, bw = x
So, w = x/b
→ Thus, acceleration is x/b [Option 3]
Hope it helps.
Purva
@Purvaparmar1405
Brainly.in
→ Here, we have been given an equation relating velocity v and distance x from origin.
♦ Let acceleration be denoted by 'w'
(The letter 'a' is already used as constant. So I'm using a different letter here)
Thus, w = dv/dt (First derivative of velocity with respect to time)
Also, v = dx/dt
→ Now, given equation is:
a + b v² = x²
(Differentiating with respect to time)
So, d(a)/dt + d(bv²)/dt = d(x²)/dt
So, 0 + b (2v) dv/dt = 2x dx/dt
[a is constant. So da/dt = 0
Now, dv/dt = w, and dx/dt = v ]
So, 2bv w = 2x v
[v is common on both sides. So cancel it]
So, bw = x
So, w = x/b
→ Thus, acceleration is x/b [Option 3]
Hope it helps.
Purva
@Purvaparmar1405
Brainly.in
Shivyaa:
thnks
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