Question

Explain the instantaneon
velocity of an object in two dimensions.​

Answer 1

Answer:

Instantaneous velocity is defined as the rate of change of position for a time interval which is very small (almost zero). Measured using SI unit m/s. Instantaneous speed is the magnitude of the instantaneous velocity. It has the same value as that of instantaneous velocity but does not have any direction.

Explanation:

In simple words, the velocity of an object at that instant of time. Instantaneous velocity definition is given as “The velocity of an object under motion at a specific point of time.”

If the object possesses uniform velocity then the instantaneous velocity may be the same as its standard velocity.

Instantaneous Velocity

It is determined very similarly as that of average velocity, but here time period is narrowed. We know that the average velocity for a given time interval is total displacement divided by total time. As this time interval approaches zero, the displacement also approaches zero. But the limit of the ratio of displacement to time is non-zero and is called instantaneous velocity.

Instantaneous Velocity Formula

The instantaneous velocity formula is given by

Vi=limΔt→0dsdt

Where,

Δt is the small-time interval.

Vi is the instantaneous velocity.

s is the displacement.

t is the time.

Unit of Instantaneous Velocity

The SI unit of instantaneous velocity is m/s. It is a vector quantity. It can also be determined by taking the slope of the distance-time graph or x-t graph.

Instantaneous Velocity Example

If the displacement of the particle varies with respect to time and is given as (6t2 + 2t + 4) m, the instantaneous velocity can be found out at any given time by:

s = (6t2 + 2t + 4)

Velocity (v) = dsdt = d(6t2+2t+4)dt = 12t + 2

So, if we have to find out the instantaneous velocity at t = 5 sec, then we will put the value of t in the obtained expression of velocity.

Instantaneous velocity at t = 5 sec = (12×5 + 2) = 62 m/s

Let us calculate the average velocity now for 5 seconds now.

Displacement = (6×52 + 2×5 + 4) = 164 m

Average velocity = 1645 = 32.8 m/s

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