if the displacement of a particle varies with time as root of x= t+7, the
a)velocity is inversely proportional to t
b)velocity is proportional to square of t
c)velocity is proportional to root of t
d)particle moves with constant acceleration
pls help...i have no idea how to solve this question
To solve this question, we need to analyze the given equation for displacement and determine the relationship between velocity and time.
The equation for displacement in terms of time, x = t + 7, suggests that the displacement of the particle is directly proportional to time. It is important to note that the square root (√) in the question does not affect our analysis since we are dealing with a direct proportional relationship.
To find the velocity, we need to differentiate the equation for displacement with respect to time. The derivative of x with respect to t gives us the rate of change of displacement, which is the velocity.
Differentiating the equation x = t + 7 with respect to t, we get:
dx/dt = d/dt(t + 7)
= 1
The derivative of t with respect to t is 1, and since the constant 7 does not depend on time, its derivative is zero. Therefore, the velocity, dx/dt, is equal to 1.
From this analysis, we can conclude that the velocity is constant and independent of time, meaning the particle moves with a constant velocity rather than a constant acceleration. Therefore, the correct answer is:
d) The particle moves with constant acceleration.
It is important to note that acceleration can be determined by differentiating velocity with respect to time. If acceleration were mentioned in the equation or if the question provided the equation for velocity, we could further analyze the particle's acceleration. However, based on the given information, we can only determine the constant velocity.