An automobile weighing 3,000 kg is driven on a track at x km/hr. Its kinetic energy, K, is given by the expression k=1/2 x 3000 x ( 1000x/3600)^2 Note that a kilometer equals 1,000 meters, and an hour equals 3,600 seconds. What is the meaning of the term (1000x/3600)^2

Question

A.
the square root of the car’s energy

B.
the change in the car’s energy

C.
the car’s speed in meters per second

D.
the weight of the car in grams

Answer 1

To understand the term \( \left(\frac{1000x}{3600}\right)^2 \), we can break down what it represents in the context of the kinetic energy formula.

1. The term \( x \) is the speed of the automobile in kilometers per hour (km/hr).
2. The expression \( \frac{1000x}{3600} \) converts the speed from km/hr to meters per second (m/s).
   • \( 1000 \) converts kilometers to meters (1 km = 1000 m).
   • \( 3600 \) converts hours to seconds (1 hour = 3600 seconds).

So, \( \frac{1000x}{3600} \) gives the speed \( v \) of the car in meters per second.

3. When we square this term, \( \left(\frac{1000x}{3600}\right)^2 \) represents the square of the car's speed in meters per second, which is essential for calculating kinetic energy.

Given this breakdown, the correct interpretation of \( \left(\frac{1000x}{3600}\right)^2 \) is:

C. the car’s speed in meters per second (specifically, it is the square of the car’s speed in meters per second).