ANSWER
75.65 km/h
EXPLANATION
Given:
• The student's mass, m = 77 kg
,• The kinetic energy of the student in the car, KE = 1.7 x 10⁴ J
Find:
• The speed read in the speedometer of the car, which is the speed of the student, v (in km/h)
The kinetic energy of an object with mass m, traveling at a speed v, is,
[tex]KE=\frac{1}{2}mv^2[/tex]Solving for v,
[tex]v=\sqrt{\frac{2KE}{m}}[/tex]Replace the known values and solve,
[tex]v=\sqrt{\frac{2\cdot1.7\cdot10^4J}{77kg}}\approx21.013m/s[/tex]Note that because the kinetic energy is given in Joules - which is equivalent to kg*m²/s², the speed we found is in m/s. Now, knowing that there are 3600 seconds in 1 hour and that 1 km is equivalent to 1000 m, we can convert this to km/s,
[tex]v=21.013\frac{m}{s}\cdot\frac{3600s}{1h}\cdot\frac{1km}{1000m}\approx75.65km/h[/tex]Hence, the speedometer reading of the car is 75.65 km/h, rounded to the nearest hundredth.
