How Do I Integrate Kinematics Problems with Units?

[noypingpogi]

hello, I'm new to the forums. Can someone help me with integrating kinematics problems? For example velocity= Be^(-rt), where B= 3.00 m/s and r=0.500 s^-1. i don't understand how the integral's unit becomes m (since the integral of velocity is displacement). someone help me! thanks

 

[A.T.]

hello, I'm new to the forums. Can someone help me with integrating kinematics problems? For example velocity= Be^(-rt), where B= 3.00 m/s and r=0.500 s^-1. i don't understand how the integral's unit becomes m (since the integral of velocity is displacement). someone help me! thanks

You forgot the unit of "t". "rt" is a dimensionless number. Velocity has the unit of "m/s", and if you integrate in respect to "t" you have to multiply this unit by "s".

 

[diazona]

$$\int B e^{rt} \mathrm{d}t = \frac{B}{r} e^{rt}$$
On the left, you have B (m/s) times dt (s), giving units of meters; on the right, B (m/s) divided by r (1/s), again giving meters. As A.T. said, the exponential part is dimensionless.

 

[noypingpogi]

yes, i figured it out. "t" is in seconds which makes e^-rt dimensionless (since s^-1 * s = 1). thanks for the help.