Comparing linear motion graphs

Cheetahs are adapted for speed as the fastest land animals, reaching faster artes than most sport cars. They have ben measured to accelerate at rates of 10 m/s^2+. A sport car can accelerate at about 7. m/s^2 and cheetahs can go from rest to 10 m/s in only three strides.

Acceleration-time graph

Like finding an object's displacement or change in position by finding the area under a velocity-time graph, an object's velocity changes from the area under an acceleration-time graph, which has the acceleration on the vertical and horizontal axis.

Figure 2 shows a cheetah's motion with points lying along a horizontal straight line with a non-zero y-intercept. The acceleration is a constant 4.0 m/s^2, so this graph represents uniform acceleration.

If the cheetah's initial velocity is 0 (it's at rest), the final velocity is equal ot the change in velcoity, 20m/s [W]. If the initial velocity is 5 m/s [W], but then the graph shows tha thte final velocity is 

5 m/s [W] =20 m/s [W] = 25 m/s [W]

The graph doesn't shows what the initial and final velocities are; just the velocity change occuring in the time interval.

Relationships of Linear Motion Graphs

Graphical analysis is among the best analytical tools for physicists. In objects' motions, analyzing position-time, velocity-time, and acceleration-time graph can show real-life events like the cheetah's motion, which is crucial as most object in nature don't have a speedometer.

The 3 graphs compare 3 types of linear motion graphs, which show the same type of motion: uniform, acceleration, but look differents. 

Problem 1: Creating a velocity-time graph from an acceleration-time graph.