Answer to Question #207970 in Classical Mechanics for Omran Fayad

Question

Two toy cars (A) and (B) move in rectilinear paths
parallel to each other.
The variation of speed V of each car with respect to
time is represented in the adjacent figure.
Initially, at to=0 , the two cars start from origin O.
1. Indicate, with justification, the nature of motion
of each car.
2. Indicate the initial speed Vo of each car.
3. Determine the acceleration a1 and a2 of car (A) and car (B)
respectively.
4. Write as a function of time the equation of speed of each car.
5. Show that the time equation of motion of each car is:
XA= t2+2t and XB= -t
2+10t .
6. Determine the position of each car at the instant when the two cars
have same speed.
7. Deduce the distance separates the two cars when they have same
speed .

Answer 1

1) A - motion with constant acceleration, B - motion with constant deceleration.

2)

$$v_A=2\frac{m}{s}\\v_B=10\frac{m}{s}$$

3)

$$a_A=2\frac{m}{s^2}\\a_B=-2\frac{m}{s^2}$$

4)

$$v_A=2+2t\\v_B=10-2t$$

5)

$$x_A=2t+t^2\\x_B=10t-t^2$$

6)

$$x_A=2(2)+(2)^2=8\ m\\x_B=10(2)-(2)^2=16\ m$$

7)

$$d=16-8=8\ m$$