A car travels at a constant speed of x miles per hour. Which of the following expressions gives the distance in miles, the car will travel in hours?

Rationale

xt gives the distance in miles the car will travel in hours.

The formula for distance when traveling at a constant speed is defined as distance = speed × time. Therefore, if a car is traveling at a speed of x miles per hour for t hours, the distance traveled can be expressed as the product of these two variables, which is xt.

A (x+t) YOUR ANSWER

This expression inaccurately adds speed and time together. Distance cannot be calculated by simply summing speed and time, as the units do not correspond to distance. Thus, this choice fails to represent the relationship between these variables correctly.

B (t+x) YOUR ANSWER

Similar to choice A, this option also combines time and speed through addition. The result of adding t and x does not yield a value representing distance, as it does not maintain the correct dimensional analysis necessary for distance calculation.

C (xt) CORRECT

This expression accurately calculates distance by multiplying speed (x miles per hour) by time (t hours). The result, xt, represents the total distance traveled in miles, adhering to the fundamental physics formula for distance.

D ((xt)²) YOUR ANSWER

This choice squares the product of speed and time, resulting in a unit of distance squared, which does not make sense in the context of calculating distance traveled. The squaring operation misrepresents the relationship between speed, time, and distance, leading to an incorrect interpretation of the distance.

Conclusion

The distance a car travels at a constant speed can be correctly expressed by the product of its speed and the time traveled, represented by the formula xt. The other options either misapply arithmetic operations or fail to maintain the correct dimensional analysis needed to derive a distance measurement. Understanding this relationship is crucial in solving physics problems related to motion.

A car travels at a constant speed of x miles per hour. Which of the following expressions gives the distance in miles, the car will travel in hours?

xt gives the distance in miles the car will travel in hours.

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