Answer to Question #260623 in Physics for Bash

Question

A body start from rest and after 20 seconds acquired a velocity of 80m/s. It then moved with constant velocity for the next 10 seconds before coming to rest in a further 15 seconds.

Draw the velocity time graph and determine:

a) The total distance covered

b) The average speed

c) The acceleration

d) The retardation

Answer 1

Let's draw the Velocity versus Time graph:

(a) The area under the Velocity vs. Time graph represents the total distance covered. Let's find the area under the graph:

$d_1=Area_{left\ triangle}=\dfrac{1}{2}bh=\dfrac{1}{2}\times20\ s\times80\ \dfrac{m}{s}=800\ m,$ $d_2=Area_{rectangle}=ab=10\ s\times80\ \dfrac{m}{s}=800\ m,$ $d_3=Area_{right\ triangle}=\dfrac{1}{2}bh=\dfrac{1}{2}\times15\ s\times80\ \dfrac{m}{s}=600\ m,$ $d_{tot}=d_1+d_2+d_3=800\ m+800\ m+600\ m=2200\ m.$

(b) The average speed can be found as follows:

$v_{avg}=\dfrac{d_{tot}}{t_{tot}}=\dfrac{2200\ m}{45\ s}=48.9\ \dfrac{m}{s}.$

(c) We can find the acceleration of the body from the slope of the Velocity vs. Time graph:

$a=Slope=\dfrac{\Delta y}{\Delta x}=\dfrac{80\ \dfrac{m}{s}-0\ \dfrac{m}{s}}{20\ s - 0\ s}=4.0\ \dfrac{m}{s^2}.$

(d) We can find the retardation of the body from the slope of the Velocity vs. Time graph:

$a=Slope=\dfrac{\Delta y}{\Delta x}=\dfrac{0\ \dfrac{m}{s}-80\ \dfrac{m}{s}}{45\ s - 30\ s}=-5.33\ \dfrac{m}{s^2}.$

The sign minus means that the body decelerates.