Answer to Question #251286 in Mechanics | Relativity for physics

Question

A man runs at a speed of 4,0m/s to overtake a standing bus. When he is 6,0 m behind the door (at t=0 s), the bus moves forward and continues with a constant acceleration of 1,2 m/s². a) Write the equation of motion ( x versus t) for both - men and bus. b) Draw these two functions x = x(t) using same coordinates system. Take t = 0s , 0.5s, 1.0s, 1.5s, 2.0s, 2.5s and 3.0s c) How long does it take for the men to gain the door? Solve this using the functions from part a.

Answer 1

a) The equations of motion:

$$x_m(t)=v_mt=4t,\\ x_b(t)=x_{b0}+\frac{at^2}2=6+0.6t^2.$$

b) The functions in the same system of coordinates:

c) Let's solve!

$$x_m(t)=v_mt=4t,\\ x_b(t)=x_{b0}+\frac{at^2}2=6+0.6t^2,\\ x_m=x_b,\\ 4t=6+0.6t^2,\\ t=2.28\text{ s}.$$