Calculating Distance Required to Overtake Another Vehicle

How to determine the distance Betty needs to drive to overtake Fred?

Acceleration is the key factor in overtaking another vehicle. With Fred driving steadily at 20 m/s and Betty accelerating, how far does Betty have to drive to overtake Fred?

Answer:

To calculate the distance Betty needs to drive to overtake Fred, we need to consider the concept of acceleration. Acceleration is the rate of change of velocity over time. In this scenario, Fred is driving at a constant speed of 20 m/s while Betty is accelerating to match his speed.

Acceleration is defined as the change in velocity divided by the time it takes for that change to occur. In other words, it is how quickly an object changes speed. Since Betty began to accelerate, her speed increased. The problem states that Fred is driving at a constant 20 m/s, so he is not accelerating. Betty, on the other hand, is.

Therefore, Betty needs to accelerate enough to match Fred's speed of 20 m/s before she can overtake him. Once Betty's speed matches Fred's, she needs to maintain that speed to overtake him. Since they both have the same speed, the problem becomes one of distance.

The distance that Betty needs to drive to overtake Fred is equal to the distance that Fred drives during the time it takes for Betty to accelerate to his speed. We can calculate this distance using the formula: d = vt, where d is the distance, v is the velocity (20 m/s), and t is the time it takes for Betty to accelerate to 20 m/s.

We do not have enough information to calculate the time it takes for Betty to accelerate to 20 m/s. Therefore, we cannot calculate the distance she needs to drive to overtake Fred.