A 100-g toy car moves along a curved frictionless track. At first, the car runs along a flat horizontal segment with an initial velocity of 2.66 m/s. The car then runs up the frictionless slope, gaining 0.186 m in altitude before leveling out to another horizontal segment at the higher level. What is the final velocity of the car if we neglect air resistance?

The final velocity of the car is 1.85 m/s

Explanation:

Hi there!

The initial kinetic energy of the toy car can be calculated as follows:

KE = 1/2 · m · v²

Where:

KE = kinetic energy.

m = mass.

v = velocity.

KE = 1/2 · 0.100 kg · (2.66 m/s) ² = 0.354 J

The gain in altitude produces a gain in potential energy. This gain in potential energy is equal to the loss in kinetic energy. So let's calculate the potential energy of the toy car after gaining an altitude of 0.186 m.

PE = m · g · h

Where:

PE = potential energy.

m = mass.

g = acceleration due to gravity.

h = height.

PE = 0.100 kg · 9.8 m/s² · 0.186 m = 0.182 J

The final kinetic energy will be: 0.354 J - 0.182 J = 0.172.

Using the equation of kinetic energy, we can obtain the velocity of the toy car after running up the slope:

KE = 1/2 · m · v²

0.172 J = 1/2 · 0.100 kg · v²

2 · 0.172 J / 0.100 kg = v²

v = 1.85 m/s

The final velocity of the car is 1.85 m/s