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Enter the values and click the 'Calculate' button to determine the instantaneous velocity of an object.
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The instantaneous velocity calculator helps you determine the velocity of an object at a particular moment, based on its displacement and time.
"The velocity of an object at a specific moment in time"
For an object moving with uniform velocity, its instantaneous velocity is equal to its constant velocity.
Instantaneous velocity is calculated using a formula that represents the limit of average velocity as the time interval approaches zero.
Instantaneous Velocity Formula:
Instantaneous Velocity = LimΔt → 0 (x(t + Δt) - x(t)) / Δt
Equivalent derivative form:
Instantaneous Velocity = dx(t) / dt
Where:
Suppose a car moves along a straight path. Find its instantaneous velocity at t = 3 seconds if its position function is:
x(t) = 5t2 + 2t + 4
Solution:
Step #1: Use the instantaneous velocity formula:
vint = dx(t) dt
Step #2: Substitute the position function:
vint = d(5t2 + 2t + 4) dt
Step #3: Compute the derivative:
vint = 10t + 2
Step #4: Substitute t = 3 s:
vint = (10 × 3) + 2
vint = 32 m/s
Thus, at 3 seconds, the instantaneous velocity of the car is 32 m/s. This indicates the car's position changes at a rate of 32 meters per second at that instant.
➥ Instantaneous Speed:
Instantaneous speed is the magnitude of instantaneous velocity.
➥ Instantaneous Velocity:
Instantaneous velocity is the rate of change of position over an infinitesimally small interval of time.
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