displacement &timeare related by t=sqtx+3.find the time taken before the velocity is reduced to zero.?
To find the time taken before the velocity is reduced to zero, we can use the given equation:
t = sqrt(x) + 3
We know that velocity is the derivative of displacement with respect to time. So, to find the velocity equation, we need to differentiate the displacement equation with respect to time (t).
Given, t = sqrt(x) + 3
Differentiating both sides of the equation with respect to t, we get:
1 = (1/2)*(1/sqrt(x))*(dx/dt) [Differentiating sqrt(x) using chain rule]
Simplifying this equation, we get:
dx/dt = 2*sqrt(x)
Now, we know that velocity (v) is dx/dt. So, the velocity equation is:
v = 2*sqrt(x)
To find the time taken before the velocity is reduced to zero, we need to find the value of x when v = 0.
0 = 2*sqrt(x)
Dividing both sides by 2, we get:
0 = sqrt(x)
Squaring both sides of the equation, we get:
0 = x
Therefore, the time taken before the velocity is reduced to zero is when x = 0. However, it's important to note that the displacement equation given, t = sqrt(x) + 3, doesn't have a solution where the time and displacement are both real numbers. Thus, there is no real time taken before the velocity is reduced to zero based on the given displacement equation.