A jogger is moving at 5 m/s as she approaches a busy street. She needs to stop in 2 seconds in order to stay safe. What average deceleration must she have in order to stop in time?
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To determine the average deceleration needed, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Here, the initial velocity (Vi) is 5 m/s, the final velocity (Vf) we want to achieve is 0 m/s, and the time (t) is 2 seconds.
Acceleration = (0 m/s - 5 m/s) / 2 s
Simplifying the equation, we get:
Acceleration = -5 m/s / 2 s
Using basic division, we find:
Acceleration = -2.5 m/s²
So, in order for the jogger to stop in 2 seconds, she needs an average deceleration of -2.5 m/s². The negative sign indicates deceleration, which means the jogger needs to slow down.
To find the average deceleration the jogger must have in order to stop in time, we need to use the equation for average acceleration:
Average acceleration = Change in velocity / Time elapsed
In this case, the jogger needs to stop completely, so her final velocity would be 0 m/s. The initial velocity is given as 5 m/s.
Change in velocity = Final velocity - Initial velocity
Change in velocity = 0 m/s - 5 m/s
Change in velocity = -5 m/s
The time elapsed is given as 2 seconds.
Average acceleration = (-5 m/s) / (2 s)
Average acceleration = -2.5 m/s^2
Since the jogger needs to decelerate to stop in 2 seconds, the average deceleration must be -2.5 m/s^2.
Note: The negative sign indicates deceleration (slowing down), whereas a positive sign represents acceleration (speeding up). In this case, the jogger is decelerating to stop.
using the kinematic equation: Vf = Vo + at
Vf = final velocity = 0m/s because she comes to a stop
Vo = initial velocity = 5m/s as she is jogging
a = acceleration (or in this case deceleration)
t = time elapsed = 2 s
so...
Vf = Vo + at
0m/s = 5m/s + a * 2s
-5m/s = a * 2s
(-5m/s)/2s = a
-2.5 m/s^2 = a
because the acceleration ends up being negative it is understood to be deceleration.