the brakes applied to a car produces uniform retardation. the car covers 16m before stopping how long where the brakes applied
Depends on how fast the car was moving at the start.
To find the time for which the brakes were applied, we can use the equation of motion for uniformly retarded motion:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 in this case, as the car comes to a stop)
u = initial velocity of the car
a = retardation (uniform in this case)
s = distance covered by the car
Given:
s = 16m
v = 0
Rearranging the equation, we get:
v^2 - u^2 = 2as
Since v = 0, the equation simplifies to:
0 - u^2 = 2as
Therefore, we have:
u^2 = -2as
Now, we can solve for u^2:
u^2 = -2as
u^2 = -2 * (retardation) * (distance)
u^2 = -2 * a * 16
To find the value of a (retardation), we need more information. If that information is not provided, we cannot specifically determine the value of a. However, we can proceed with arbitrary values for demonstration purposes.
Let's assume a retardation value of a = -2 m/s^2.
u^2 = -2 * 2 * 16
u^2 = -64
u = √(-64)
u = 8i or -8i (where i is the imaginary unit)
Since we are interested in the magnitude of the velocity, we take the positive value, so u = 8 m/s.
Now, we can find the time taken:
v = u + at
Rearranging the equation, we have:
t = (v - u) / a
t = (0 - 8) / (-2)
t = 8 / 2
t = 4 seconds
Therefore, if the retardation is assumed to be -2 m/s^2, then the brakes were applied for 4 seconds to cover a distance of 16 meters and bring the car to a stop.