A common graphical representation of motion along a straight line is the v vs. t

Question

A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call v the velocity and a the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively.

What is the total distance x traveled by the particle?

I know that the answer in 75 m but could someone explain to me where each number comes from in the equation? Please go step by step.

Explanation / Answer

0.5*20*(2-0.5) + (20*0.5) + (20*2)+0.5*(50-40)*2

here,

in such type graphs you must see the area under the cureve

distance, x = area under the cureve

distance, x = area of triangle + area of rec under previous triangle + area of middle rectangle + area of remaining region

distance, x = ( 0.5*base*height + length * height ) + (length * height) + (0.5*base*height)

distance, x = 0.5*20*(2-0.5) + (20*0.5) + (20*2) + 0.5*(50-40)*2

distance, x = 75 m

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