Show that area under velocity-time curve of body moving uniformly gives the displacement of the particle in a given time.
Answers
Answer:
If a body has uniform motion then the line on the graph will be straight and parallel to the x axis. the area of that part of the graph would be either the square of a rectangle or a square
velocity =diplacement/time
area of part covered by line =lenght*breadth
therefore, velocity multiplied by time= displacement\time *time/1
displacement=s
time=t
s/t*t=s
=displacement
if the body is moving in a uniform fashion then you can easily calculate the distance covered by the body in 1 second
hope this helps.if you need any more help please reach out
Answer:
The above figure represent the velocity curve. The horizontal line represent the constant velocity. The line with slope represent the constant acceleration. Now the area under the constant velocity curve is utut. The are under the triangle is 12×(v−u)×t=12at212×(v-u)×t=12at2 considering a as constant acceleration. So the total area under the curve is A=ut+12at2A=ut+12at2. Which is the distance travelled by a particle moving with constant acceleration a and initial velocity v. Hence proved.