if the displacement of a particle varies with time as root of x=t+7 what is the relation between the velocity and time
d= sqrt(t+7)
v=D d/dt=1/2(t+7)
To determine the relation between velocity and time, we need to differentiate the given expression for displacement with respect to time (x = √(t + 7)) to find the velocity.
Step 1: Differentiate the displacement equation with respect to time.
(dx/dt) = d(√(t + 7))/dt
Step 2: Apply the chain rule to differentiate the square root function.
(dx/dt) = (1/2) * (t + 7)^(-1/2) * 1
Step 3: Simplify the expression.
(dx/dt) = 1/2√(t + 7)
Thus, the relation between velocity (v) and time (t) is:
v = dx/dt = 1/2√(t + 7)
Therefore, the velocity is equal to 1/(2 times the square root of the quantity t plus 7).