Average Acceleration Units Problem

[nivekov123]

1. An electric train initially moving at 25km/h accelerates to 35km/h in 20s. Find its average acceleration in m/s^2.
G: v1 = 25km/h
v2 = 35km/h
Delta t = 20s
R: A_av




2. A_av=(v2-v1)/delta t





3. = (35km/h-25km/h)-20s
The problem is that the velocities are in km per hour and the change in time is seconds. Do I just continue on with the question as is? Or if I had to convert the velocities to m/s how would i do so to divide with the 20s so that i may end up with a = m/s^2 ?

 

[happysmiles36]

You would need to change the km/h to m/s and to do that you need to do unit analyses.
u put them in fraction form first so

km 1000m...h ...1000m
__x______x______=_______
h ...km ...3600s ...3600sin 1 km there is 1000m so you divide km by km to cancel it out and multiply the original km by 1000m
in 1 h there is 3600s (60x60) so you divide by h to cancel h out and multiply it by 3600s

then divide your m by 3600s and you have your m/s

after you've done that just follow the formula for average acceleration. (Aave=(v^2-v^1)/Delta t)Example:

v=10 km/h
t=5.0s

10 km/h / km x 1000m / h x 3600s= 10000m/3600s = 2.77777...m/s

a= 2.777..m/s / 5.0s
a= 0.555...m/s^2
a= 0.56 m/s^2 (significant digits) <---Final Answer