Answer to Question #96198 in Mechanics | Relativity for AbdulRehman

Question

Suppose that your car is parked in front of a house. You get in, start
the engine, and drive away. You step on the gas until the speedometer
increases to 30mph, then you hold that reading constant.
Draw two spacetime diagrams, each showing both the house and the car.
Draw one in your own frame of reference, and draw the other in the house’s
frame of reference. Be sure to label both diagrams with an appropriate scale

Answer 1

1) Consider the driver in the car. As time passes, he does not with regard to the car, so the driver's displacement is 0, but time goes and goes. The driver's spacetime diagram is the blue line (only first 60 seconds).

2) Consider someone sitting in the house and measuring distance to the car. Assume that the uniform acceleration was 1 m/s/s, and after the 5th second the car's velocity is 30 mp/h. The observer will see the car moving off initially with acceleration, and then with constant speed. Initially, first 5 seconds, the distance vs. time was a parabola

$$d_a(t)=at^2/2,$$

after the 5th second the distance vs. time was simply an inclined line

$$d_b(t)=vt$$

The observer's spacetime diagram is the red line (only first 60 seconds):