as she climbs a hill, a cyclist slows down from 25mi/hr to 6mi/hr in 10 seconds. what is her deceleration? my answer is -1.9 is this correct or should it be a positive 1.9...am confused

Here is my mathematical approach

physics has nice formulas for this

v = at + c
when t = 0, v = 25
so 25 = 0+c
c = 25

then v = at + 25
when t = 10 , v = 6
6 = 10a + 25
10a = -19
a = -1.9

Whenever you see the word deceleration (things slow down) you can expect a negative result, just like for acceleration you can expect a positive answer.

To calculate the deceleration, we need to determine the change in velocity and the time taken. The change in velocity is the difference between the initial velocity and the final velocity, and the time taken is given as 10 seconds.

Given:
Initial Velocity (u) = 25 mi/hr
Final Velocity (v) = 6 mi/hr
Time (t) = 10 seconds

To find the deceleration (a), we can use the formula:

a = (v - u) / t

Substituting the given values:

a = (6 - 25) / 10
a = (-19) / 10
a = -1.9

So, your answer of -1.9 is correct. The negative sign indicates deceleration, also known as acceleration in the opposite direction. Therefore, there is no need to change the sign to be positive 1.9.

To find the deceleration, you need to calculate the change in velocity and divide it by the time taken. In this case, the change in velocity is the difference between the initial velocity and the final velocity.

Given:
Initial velocity (u) = 25 mi/hr
Final velocity (v) = 6 mi/hr
Time taken (t) = 10 seconds

Change in velocity (Δv) = Final velocity (v) - Initial velocity (u)
= 6 mi/hr - 25 mi/hr
= -19 mi/hr

Note that the negative sign indicates a decrease in velocity, or deceleration.

Deceleration (a) = Change in velocity (Δv) / Time taken (t)
= -19 mi/hr / 10 seconds
= -1.9 mi/hr^2

Therefore, the correct deceleration is -1.9 mi/hr^2. The negative sign indicates deceleration or a decrease in speed.