Answer:
The car can have a maximum acceleration of 2.55 m/s² without causing the cup to slide.
Step-by-step explanation:
When the car is in motion, there are two forces acting on the cup. First force is exerted by the car on the cup in its direction of motion and it is given by newton's second law of motion:
F = ma
The second force is the force of friction between the surface of car and the cup. It is given by the formula:
f = μR
where,
R = Normal reaction = weight of cup = W = mg
Therefore,
f = μmg
So, for the cup not to slide, both these forces must be equal or the frictional force must be greater than the car's force. In the last limiting case of equal forces:
F = f
ma = μmg
a = μg
where,
a = maximum possible acceleration of the car for cup not to slide
μ = coefficient of static friction = 0.26
g = acceleration due to gravity = 9.8 m/s²
Therefore,
a = (0.26)(9.8 m/s²)
a = 2.55 m/s²