Instantaneous velocity at a given time-instant for a particle can be found from the y-intercept of its velocity-time graph. From a particle's velocity-time graph, its average velocity can be found by calculating the total area under the graph and then dividing it by the corresponding time-interval. For a particle with uniform acceleration, velocity-time graph is a straight line. Its average velocity is given by vavg=(vi+vf)/2. From the graph, this can be found by drawing the y-intercepts of initial and final velocities and then drawing the mid-point. In the given graph, instantaneous velocity =v1 at t=t1 and v2 at t=t2. Average velocity is found at E, i.e. mid-point of C and D.
Acceleration from velocity-time graph
Acceleration of a particle is equal to the slope of a velocity-time graph. a=t2−t1v2−v1 In the given graph, a=4−240−20=10m/s2 Acceleration may be positive, negative or zero as it is a vector quantity.
Displacement from velocity-time graph
Displacement of a particle in a given time-interval is equal to the total area under the velocity-time graph in the given time-interval. In the given graph, displacement is found as area of trapezium ABCD. s=21×DC×(AD+BC) Note: Since, displacement is a vector quantity, Area below the time-axis is considered as negative and above it is considered as positive.
Area under acceleration time graph
Change in velocity of a particle can be evaluated as area under the acceleration-time graph.
as a=dtdv or dv=adt or Velocity=∫adt (Which is area under the curve.)
Velocity Time graph for rest, uniform motion and uniform acceleration
The Velocity Time Graph: Velocity-time graph is a plot between Velocity and Time. It shows the Motion of the object that moves in a Straight Line. Magnitude of Velocity at a given instant is equal to its Instantaneous Speed. It is drawn for 1-D motion only and can take both positive and negative values.
In case where the acceleration is zero, tthe slope is zero ( horizontal line). If the acceleration is positive, then the slope is positive (an upward sloping line).