The brakes of an automobile are suddenly applied at the instant when its velocity is 20 m/s. If the automobile comes to a stop after 5 seconds, what is its acceleration?
Well, let's brake it down, shall we? The initial velocity of the automobile is 20 m/s, and it comes to a stop after 5 seconds. So, we're basically trying to find the rate at which the velocity changes, which is the definition of acceleration. Now, without any clowning around, let's calculate!
Using the equation for acceleration (a = Δv/Δt), where Δv is the change in velocity and Δt is the change in time, we can find the acceleration.
Since the automobile goes from 20 m/s to 0 m/s, the change in velocity (Δv) is 0 - 20 = -20 m/s. And the change in time (Δt) is 5 seconds. So, the acceleration (a) is -20 m/s divided by 5 seconds.
Therefore, the acceleration of the automobile is -4 m/s². Or, in other words, the automobile is slowing down at a rate of 4 meters per second squared. I hope that answer brakes the intensity of your question!
To find the acceleration of the automobile, we can use the equation of motion:
v = u + at,
where:
v = final velocity (0 m/s, since the automobile comes to a stop)
u = initial velocity (20 m/s)
a = acceleration
t = time taken (5 seconds)
Rearranging the equation to solve for acceleration (a), we have:
a = (v - u) / t.
Substituting the given values:
a = (0 m/s - 20 m/s) / 5 s.
Simplifying the equation:
a = (-20 m/s) / 5 s.
This gives us:
a = -4 m/s².
Therefore, the acceleration of the automobile is -4 m/s².
To find the acceleration of the automobile, we can use the kinematic equation:
v = u + at
Where:
v = final velocity (0 m/s, since the automobile comes to a stop)
u = initial velocity (20 m/s)
a = acceleration (unknown)
t = time (5 seconds)
Rearranging the equation to solve for acceleration (a):
a = (v - u) / t
Substituting the values into the equation:
a = (0 m/s - 20 m/s) / 5 s
a = -20 m/s / 5 s
a = -4 m/s^2
Therefore, the acceleration of the automobile is -4 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, contributing to the deceleration of the automobile.
v = Vi + a t
0 = 20 + 5 a
a = - 4 m/s^2