In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
1. | The average velocity is not zero at any time. |
2. | The average acceleration must always vanish. |
3. | The displacements in equal time intervals are equal. |
4. | Equal path lengths are traversed in equal intervals. |
Hint: The magnitude of instantaneous velocity is equal to the speed.
Explanation: Speed (Instantaneous Speed): The magnitude of the velocity at any instant of time is known as the instantaneous speed or simply speed at that instant of time. It is denoted by \(v.\)
\(\Rightarrow \text{Speed }= \dfrac{\text{Distance}}{\text{Time}}\)
Mathematically, it is the time rate at which distance is being travelled by the particle.
Speed is a scalar quantity. It can never be negative (as shown by the speedometer of our vehicle). The instantaneous speed is the speed of a particle at a particular instant of time.
Hence, \(\text{Total distance travelled}=\text{Path length }=\text{( Speed ) }\times\text{Time taken}\)
Therefore speed is related to the total distance covered not the displacement.
Hence, option (4) is the correct answer.
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