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.
physics
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 solve this problem, we can use the concept of acceleration due to friction and the equation of motion.
The formula to calculate acceleration due to friction is:
acceleration = coefficient of kinetic friction × gravitational acceleration
In this case, we need to calculate the acceleration in order to find the change in velocity after 1.21 seconds.
Given:
Initial speed (u) = 19.5 m/s
Time (t) = 1.21 s
Coefficient of kinetic friction (μ) = 0.740
First, calculate the acceleration using the formula:
acceleration = μ × gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
acceleration = 0.740 × 9.8m/s^2
Next, use the equation of motion to find the final velocity (v):
v = u + (acceleration × t)
Substitute the known values into the equation:
v = 19.5 m/s + (acceleration × 1.21 s)
Calculate the value of acceleration using the previous step, then substitute it into the equation:
v = 19.5 m/s + (acceleration × 1.21 s)
Finally, calculate the final velocity:
v = ?
Once you have found the value of v, you will have the speed of the automobile after 1.21 s have elapsed.