The displacement x of a particle in meters along the x- axis with time ‘t’ in seconds according to the equation-

(a) draw a graph if x versus t for t = 0 and t =5 sec
(b) What is the displacement come out of the particles initially?
(c) What is slope of the graph obtained?

Question

Answer

Answer:

Given Information

The displacement x of a particle in meters along the x-axis with time ‘t’ in seconds according to the equation:

x = 3t + 2t^2

Graph

(a) Draw a graph of x versus t for t = 0 and t = 5 sec:

If t = 0, x = 3(0) + 2(0)^2 = 0

If t = 5, x = 3(5) + 2(5)^2 = 55

So the points on the graph are (0,0) and (5,55). The graph is a parabola opening upwards.

Initial Displacement

(b) What is the displacement come out of the particles initially?

The initial displacement is the value of x when t = 0, which is 0. So the particle starts at the origin.

Slope of the Graph

(c) What is the slope of the graph obtained? Explain in detail.

The slope of the graph is the rate of change of displacement with respect to time, which is the velocity of the particle. The velocity can be found by taking the derivative of the displacement function:

v = dx/dt = 3 + 4t

At t = 0, v = 3. So the particle starts with a velocity of 3 m/s. The slope of the graph is the velocity at any point, so it varies with time. At t = 5, v = 3 + 4(5) = 23 m/s. So the slope of the graph at t = 5 is 23.

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