The instantaneous velocity of an object is basically the average velocity by taking the limit (change in temperature)Δt →0.
In the present-day formula one race weekend, one car can reach speeds of up to 200 miles per hour, but when the five red lights come off, all the awaiting drivers are morally and physically equal. The initial velocity of the drivers is zero before they press the gas pedal. We could indeed say that the velocity of these cars changes over time at different points. As they approach the checkered flag, the best of these drivers reach their top velocity. Source
The formula of the instantaneous velocity is expressed mathematically by using the formula for the average velocity.
Average velocity (V) = x(t2) - x(t1) ( net displacement ) / t2 - t1 ( net time)
In order to find the instantaneous velocity at an arbitrary position, we assume t1= t and t2= t+Δ t. After using these values in the formula of the average velocity, we take the limit as
Δt →0 and find the expression of the instantaneous velocity
The slope of the distance-time graph, often known as the x-t graph, can also be used to determine it.
An example of the instantaneous velocity can be
If the object's displacement changes with time and therefore is given as (5t2+3t+4) m, the instantaneous velocity can be calculated at any time by:
s= (5t2+3t+4) Velocity (v) = 10t+3 So, if we need to calculate the instantaneous velocity at t = 10 seconds, we'll plug the constant into the velocity expression.
Therefore the instantaneous velocity at t=10 s will be 103 m/s The displacement, in this case, will be 534 meters ( using the values of t in the given expression )
And the average velocity will be 534/10= 53.4 m/s.
1. Write the expression for instantaneous velocity.
The mathematical expression for the instantaneous velocity will be v ( instantaneous) = limit Δt →0 ds/dt, where ds is net displacement, and dt is the net time.
2. What do you understand about instantaneous velocity?
The instantaneous velocity can be easily understood as the velocity of a moving item at a certain moment in time.
3. How to calculate instantaneous velocity?
The instantaneous velocity can be calculated using v ( instantaneous) = limit Δt →0 ds/dt, where ds is net displacement and dt is the net time.
4. When will the average velocity be equal to instantaneous velocity?
In a motion where an object moves with constant velocity, the average and the instantaneous velocity will be equal.
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