Question

Physics students learning about potential and kinetic energy perform an experiment with a toy car rolling down a sloped track. They use high-speed cameras to measure the velocity of the car at different heights on the track. They use the height data to calculate the kinetic energy of the car, in joules. Then, they plot their data on a scatter plot of kinetic energy (y) versus velocity (x) in meters per second and fit a quadratic function to the data.

The equation of the function is y=0.3155xsquared-0.2152x+0.1445 According to this model, what is the approximate kinetic energy of the car when it is moving at a velocity of 4 meters per second?
 
 
A. 1.8 joules
 
B. 3.9 joules
 
C. 4.3 joules
 
D. 6.1 joules

Answer 1

Compute y = 0.3155(4^2) − 0.2152(4) + 0.1445.
4^2 = 16 → 0.3155·16 = 5.048
−0.2152·4 = −0.8608
So y = 5.048 − 0.8608 + 0.1445 = 4.3317 ≈ 4.3 J.

Answer: C (4.3 joules).