Traveling at a speed of 19.5 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 0.740. What is the speed of the automobile after 1.21 s have elapsed? Ignore the effects of air resistance.
Deceleration=0.74*10=7.4m/s^2 v-u=at v-19.5=-7.4 v=-7.4+19.5=12.1m/s
To find the speed of the automobile after 1.21 seconds have elapsed, we can use the equations of motion. We'll use the equation that relates the final velocity of an object with its initial velocity, acceleration, and time:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the initial velocity (u) is 19.5 m/s and the time (t) is 1.21 seconds. We need to find the acceleration (a), and then we can calculate the final velocity (v).
The acceleration can be determined using the equation for the force of friction, which is given by:
F = μN
Where:
F = force of friction
μ = coefficient of kinetic friction
N = normal force
Since the automobile is not accelerating vertically, the normal force (N) is equal to the weight of the car (mg), where m is the mass of the car and g is the acceleration due to gravity.
In this case, the mass of the car is not given, but we don't need it to find the acceleration. Dividing both sides of the equation F = μN by mass (m), we get:
a = (μN) / m
Now we can substitute the values given:
μ = 0.740 (coefficient of kinetic friction)
Acceleration due to gravity, g ≈ 9.8 m/s^2
We can now calculate the acceleration using the above equation.
a = (0.740)(mg) / m
a = 0.740g
Substituting this value of acceleration (a) and the initial velocity (u) into the equation for final velocity (v), we get:
v = u + at
v = 19.5 + (0.740g)(1.21)
Using the acceleration due to gravity, g = 9.8 m/s^2:
v = 19.5 + (0.740 * 9.8) * 1.21
Now, we can simply compute the final velocity by evaluating the expression.
v ≈ 19.5 + 9.603
v ≈ 29.103
Therefore, the speed of the automobile after 1.21 seconds have elapsed is approximately 29.103 m/s.