Question

Two bicycles have the following equations of motion: x1=-4.0m+2.5m/s x2=6.7m+-3.5m/st Which bicycle has the greater speed? Calculate the distance between the bicycles at t=0 and at t=1s

Answer 1

The first Bicycle has a greater speed than the second bicycle. The distance between the bicycles at t = 0 sec is 10.7m, at t = 1 sec 4.7 m.

Solving equations of motion.

Equations of motions are used to explain the speed or velocity, acceleration, position of an object with respect to time. The equations of motion of the two bicycles can be properly represented as a function of time as follows:

1. 1st Bicycle:
   `x_1 = -4.0 m + 2.5 m/s * t`
2. 2nd Bicycle:
   `x_2 = 6.7 m + (-3/5 m/s)* t`

The bicycle with the greater speed can be determined by finding the greater coefficient of the two bicycle.

Thus, the first Bicycle has a greater speed than the second bicycle. This is because it has a greater positive magnitude than the second one.

The distance between the bicycles at t = 0 and at t = 1 can be calculated as follows:

When t = 0:

`x_1 (0)= -4.0 m + 2.5 m/s * 0 = - 4.0 m \\ \\ x_2 (0)= 6.7 m +(-3.5m/s ) * 0 = 6.7 m`

`At \ t = 0 ; |x_1-x_2| = |-4.0m -6.7m| = 10.7 m`

`x_1 (1)= -4.0 m + 2.5 m/s * 1 = -1.5 m \\ \\ x_2 (1)= 6.7 m +(-3.5m/s ) * 1= 3.2m`

`At \ t = 1 ; |x_1-x_2| = |-1.5m -3.2m| = 4.7 m`

Thus, the distance between the bicycles at t = 0 sec is 10.7m, at t = 1 sec 4.7 m.