Question:
Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by XP(t) = αt + βt2 and XQ(t) = ft – t2. At what time, both the buses have same velocity?
Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by XP(t) = αt + βt2 and XQ(t) = ft – t2. At what time, both the buses have same velocity?
Updated On: Jul 8, 2024
- \(\frac{α-f}{1+β}\)
- \(\frac{α-f}{2(β+1)}\)
- \(\frac{α-f}{2(1+β)}\)
- \(\frac{f-α}{2(1+β)}\)
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The Correct Option is A
Solution and Explanation
The correct option is(D): \(\frac{f-α}{2(1+β)}\)
XP = αt + βt2
XQ = ft – t2
∴ VP = α + 2βt
VQ = f – 2t
∵ VP = VQ
⇒ α + 2βt = f – 2t
⇒ \(t=\frac{f-α}{2(1+β)}\).
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.