Understanding the Situation

* Two cars (A and B) start from rest: This means their initial velocities are zero (v₀ = 0).

* Constant acceleration: Both cars experience the same rate of change in velocity.

* Radar measures velocity: This gives us the instantaneous speed of each car at a specific moment.

* Car A is twice as fast as car B: This means the velocity of car A is double the velocity of car B at the instant the radar measurement is taken.

Setting up the Problem

Let's use the following variables:

* vA: Velocity of car A

* vB: Velocity of car B

* a: Constant acceleration (the same for both cars)

* t: Time elapsed

Using the Equations of Motion

We can use the following equation of motion, which relates velocity, initial velocity, acceleration, and time:

* v = v₀ + at

Since both cars start from rest (v₀ = 0), the equation simplifies to:

* v = at

Applying the Information to the Problem

1. Car A is twice as fast as car B:

* vA = 2vB

2. Using the equation of motion for both cars:

* vA = at

* vB = at

Solving for Time

Now we have two equations and two unknowns (vA and vB). We can solve for the time (t) when the radar measurement was taken:

1. Substitute vA = 2vB into the equation vA = at:

* 2vB = at

2. Since vB = at, we can substitute this into the equation above:

* 2(at) = at

3. Simplify and solve for t:

* 2at = at

* 2at - at = 0

* at = 0

* Since acceleration (a) is constant and not zero, the only way this equation can be true is if t = 0.

Conclusion

This means the radar measurement was taken at the very instant the cars started moving (t = 0). At that instant, both cars would have a velocity of zero, even though car A was found to be moving twice as fast as car B. This is because the radar measurement is an instantaneous reading, and at the very beginning of their motion, both cars are still at rest.