Traveling at a speed of 19.3 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the road is 0.620. What is the speed of the automobile after 1.46 s have elapsed? Ignore the effects of air resistance.
ma=μmg
a=μg
v=v₀-at,
To find the speed of the automobile after 1.46 seconds, we can use the concept of acceleration. First, let's find the acceleration experienced by the car.
The acceleration (a) can be calculated using the formula:
a = (μ * g)
where μ is the coefficient of kinetic friction and g is the acceleration due to gravity (approximately 9.8 m/s²).
Plugging in the given value, we get:
a = (0.620 * 9.8) = 6.076 m/s²
Now, we can use the equation for constant acceleration to find the final velocity (v) of the car. The equation is:
v = u + a * t
where u is the initial velocity and t is the time elapsed.
Given:
u = 19.3 m/s (initial velocity)
t = 1.46 s (time elapsed)
a = 6.076 m/s² (acceleration)
Substituting the values, we have:
v = 19.3 + 6.076 * 1.46
Calculating the equation, we find:
v = 19.3 + 8.881696
v = 28.18 m/s
Therefore, the speed of the automobile after 1.46 seconds is approximately 28.18 m/s.