(from Arons) Cars A and B travel along the same straight track. Car A is located at position s= 0.20 m at clock reading t= 0.0 s, and it maintains a constant speed of v= 0.17 m/s. Car B is located at position s=0.0 m at clock reading t= 0.04 s, and it maintains a constant speed of v= 0.80 m/s. At what clock reading will car B overtake car A?
To find the clock reading at which car B overtakes car A, we need to determine when the positions of the two cars are the same.
Let's start by determining the position of car A at any given clock reading using the equation:
s_a = s_0 + v_a * t_a
Where:
s_a is the position of car A
s_0 is the initial position of car A (0.20 m)
v_a is the constant speed of car A (0.17 m/s)
t_a is the clock reading of car A
Similarly, we can determine the position of car B at any given clock reading using the equation:
s_b = s_0 + v_b * t_b
Where:
s_b is the position of car B
s_0 is the initial position of car B (0.0 m)
v_b is the constant speed of car B (0.80 m/s)
t_b is the clock reading of car B
Since we want to find the clock reading when car B overtakes car A, we can set their positions equal to each other and solve for t_b:
s_b = s_a
s_0 + v_b * t_b = s_0 + v_a * t_a
0 + (0.80 m/s) * t_b = 0.20 m + (0.17 m/s) * t_a
0.80 t_b = 0.20 + 0.17 t_a
t_b = (0.20 + 0.17 t_a) / 0.80
Now, we can substitute the known values to find t_b:
t_b = (0.20 + 0.17 * 0) / 0.80
t_b = 0.20 / 0.80
t_b = 0.25 s
Therefore, car B will overtake car A at a clock reading of 0.25 seconds.