# Dimensional Analysis (University Physics)?

1) The acceleration (a) of an object is given by the equation a=At=Bt^2 , where t refers to time. what are the dimensions of A and B?

2) The speed, v, of an object is given by the equation v=At^3-Bt, where t is time. What are the dimensions of A and B?

Note: I was told making A and B the subject of the formula was the wrong approach as well as simultaneous equations

Relevance

1. a ~ m/s^2; so AT ~ m/s^2 and BT^2 ~ m/s^2 also.

So we have AT ~ As ~ m/s^2 and A ~ m/s^3. ANS. And BT^2 ~ Bs^2 ~ m/s^2 and B ~ m/s^4. ANS.

You should learn that units can be operated on just like variables: add, subtract, multiply and divide. In both these cases, we divided the time units.

2. v ~ m/s; so At^3 ~ m/s and As^3 ~ m/s so that A ~ m/s^4; and Bs ~ m/s; so B ~ m/s^2. ANS.

Note each of the two terms must have the same units as the LHS of the equation, the dependent variable v.

• acceleration has units m*s^-2.

the units of time is seconds. so something times seconds has the units of acceleration. What are these units?

Now repeat for B and 2).