Question

If x= 5t^2 calculate velocity​

Answer 1

Answer:

The velocity will be given by 10t where t is the time.

Explanation:

The given expression for displacement is

$x = 5t^{2}$

where t is the time and x is the displacement.

We need to evaluate the velocity in terms of time, t.

The shortest distance between the end and initial places is called displacement. Displacement is different from distance. The distance cannot be zero, but displacement can be zero.

And Velocity is the time rate change of displacement. Velocity is a vector quantity.

The derivative of displacement with respect to time is used to calculate velocity.

Thus, we have

$v = \frac{dx}{dt} = \frac{d(5t^{2}) }{dt} = 10t$

Therefore, the velocity will be given by 10t where t is the time.

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Answer 2

Answer:

v=10t

Explanation:

Step 1: The definition of velocity is the rate at which a body moves in a certain direction. Velocity is the rate at which a distance changes in relation to time. A vector quantity with both magnitude and direction is velocity.

Step 2: Velocity may be defined as the rate at which something moves in a certain direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. A vector number known as velocity describes "the pace at which an item changes its location." Imagine a person moving quickly, taking one stride ahead, one step back, and then beginning from the same place each time.

Step 3: Velocity function can be calculated by differentiation of displacement function with respect to time.

Let velocity in time t be v.

$\begin{aligned} & x=5 t^2 \\ & \Longrightarrow v=\frac{d x}{d t} \\ & \Longrightarrow v=\frac{d\left(5 t^2\right)}{d t} \\ & \Longrightarrow v=5 \frac{d\left(t^2\right)}{d t} \\ & \Longrightarrow v=5 \times 2 t \\ & \Longrightarrow v=10 t\end{aligned}$

So, velocity in time 't' is 10t.

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