Question

What Velocity vs. Time Graphs Can Tell You 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 | Figure 1 of 1 Um/s) 2.0 1.5 1.0 0.5 01 10 20 3040 50 Co Le to search

What is the total distance traveled by the particle in meters? Thank you for your time.

Answer 1

Given

graph is Vx vs t graph

we know that the displacement from the v vs t graph is area under the curve

because we know that v = d/t ==? d = v*t

from the given graph  

calculating the area under the curve we get by dividing the graph in to 4 sections namely 1,2,3,4

area of section 1 , A1 = 0.5 m/s*20 s = 10 m

area of section 2 , A2 = 0.5*20s*1.5 m/s = 15 m

area of section 3 , A3 = 2 m/s*20 s = 40 m

area of section 4 , A4 = 0.5*10s*2 m/s = 10 m

total area is A1+A2+A3+A4 = 10+15+40+10 = 75 m

so the distance travelled is 75 m