Enter the values and click the 'Calculate' button to determine the instantaneous velocity of an object.
This instantaneous velocity calculator is used to calculate the velocity of an object at a particular instance for the given displacement and time.
"A velocity of an object at a given moment in time"
When an object moves with a uniform velocity, then its instantaneous velocity will be equal to the standard velocity.
It can be calculated using a formula that shows the instantaneous velocity which is the limit of the average velocity when the time interval tends towards zero.
Instant Velocity Formula:
Instantaneous Velocity = LimΔt → 0 x(t + Δt) - x(t) Δt
From the equation:
Instantaneous Velocity = dx (t) dt
Where:
Suppose a car is moving along a straight path. Find how fast it is going at a specific moment by having a time of 3 seconds.
Car position is given by a function as:
x(t) = 5t2 + 2t + 4
Solution:
Step # 1: Use the Instantaneous velocity formula:
vint = dx(t) dt
Step # 2: Put the values into the formula:
vint = d(5t2 + 2t + 4) dt
Step # 3: Simplify the derivative
vint = 10t + 2
Put the value of (t)
vint = (10 * 3) + 2
vint= 32 ms-1
Hence, at 3 seconds the instantaneous velocity of a car is 32 ms-1. This means that the car’s position is changing at a rate of 32 meters every second at a specific moment.
➥ Instantaneous Speed:
Instantaneous speed is said to be the magnitude of instantaneous velocity
Speedint = ds dt
➥ Instantaneous Velocity:
Instantaneous velocity is the change of position which takes place at a small change in time
Vint = dx dt
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