A toy car of mass m is pushed across a horizontal surface. The push gives the toy car a starting speed of 3.50 m/s. The coefficient of kinetic friction (μk) between the toy car and the surface is 0.250. Determine how far the toy car will travel before stopping
We can use the equation for the distance traveled by a moving object with constant acceleration:
d = (v^2 - u^2) / 2a
where d is the distance, v is the final velocity (0 m/s when the car stops), u is the initial velocity (3.50 m/s in this case), and a is the acceleration (caused by friction).
The frictional force acting on the car is given by:
f = μkmg
where μk is the coefficient of kinetic friction, m is the mass of the car, and g is the acceleration due to gravity (9.81 m/s^2).
The force of friction is opposite in direction to the motion of the car, so it acts to decelerate the car. Therefore, the acceleration caused by friction is:
a = -f / m = -μkmg / m = -μkg
Substituting this into the equation for distance, we get:
d = (0^2 - 3.50^2) / (2 x (-μkg))
d = 12.25 / (2μkg)
d = 12.25 / (2 x 0.250 x m x 9.81)
Since we don't know the mass of the car, we can't calculate the exact distance traveled. However, we can see that the distance is proportional to the inverse of the mass, meaning that a heavier car would travel a shorter distance before stopping.