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4. (Progress Check Unit1-4) Toy car

\mathbf{W}

travels across a horizontal s...

Sep 26, 2024

Solution

For car W, we can use the equation of motion:

x_W = x_{0W} + v_{0W} t + \frac{1}{2} a_W t^2

. Since car W starts from rest,

v_{0W} = 0

, simplifying to

x_W = \frac{1}{2} a_W t^2

For car Z, we also use the equation of motion:

x_Z = x_{0Z} + v_{0Z} t + \frac{1}{2} a_Z t^2

. Similarly, since car Z starts from rest,

v_{0Z} = 0

, simplifying to

x_Z = x_{0Z} + \frac{1}{2} a_Z t^2

The cars will meet when their positions are equal, so we set

x_W = x_Z

. This gives us the equation:

\frac{1}{2} a_W t^2 = x_{0Z} + \frac{1}{2} a_Z t^2

. We can solve for time

t

and then substitute back to find the meeting position

The correct approach is to use the known distance

d

between the two cars to relate their positions. We can express the distance as

d = x_Z - x_W

, allowing us to find the time at which they meet and subsequently the position. Thus, option (B) is the most appropriate

Answer

Key Concept

Kinematics: The equations of motion relate displacement, initial velocity, final velocity, acceleration, and time. The key equations are:

x = x_0 + v_0 t + \frac{1}{2} a t^2

for both cars, and the relationship between their positions at the meeting point.

Explanation

By setting the equations for both cars equal to each other and using the known distance between them, we can solve for the time and position where they meet. This approach effectively eliminates unknowns and allows us to find the solution.