1. A) A ball sits motionless on the ground
Newton's First Law of inertia states that:
"When the forces acting on an object are balanced, the object stays at rest (if it was at rest) or continues its motion with constant velocity (if it was in motion)"
Among the options given, we see that the option
A) A ball sits motionless on the ground
is an example of this law: in fact, the ball sits at rest on the ground, the forces acting on it are balanced, so the ball stays at rest.
2. B) The earth pulls more on the shuttle
The gravitational attraction exerted by a planet on the shuttle is given by
\(F=G\frac{Mm}{r^2}\)
where
G is the gravitational constant
M is the mass of the planet
m is the mass of the shuttle
r is the distance between the shuttle and the planet
In this problem, we are comparing the gravitational pulls exerted by the Earth and the Moon on the shuttle. The distance, r, is the same (because the shuttle is half-way), the mass of the shuttle m is the same, and G is the same. However, the mass of the Earth is greater than the mass of the Moon, so in the formula M is greater for the Earth: therefore, the Earth pulls more on the shuttle.
3. B) The velocity of the car reduced from 50 km/h to 35 km/h over one minute
The acceleration of the car is defined as the ratio between the change in velocity and the time taken:
\(a=\frac{v_f-v_i}{\Delta t}\)
where vf is the final velocity, vi is the initial velocity, and \(\Delta t\) is the time taken.
In order to have a negative acceleration, the numerator must be negative: this means that the initial velocity, vi, must be greater than the final velocity, vf, and this situation occurs in option B), since the initial velocity is 50 km/h while the final velocity is 35 km/h.
