Question

the velocity v of a particle varies with time t according to the relation v=at^2+bt+c . find the dimensions of a, b, and c​

Answer 1

Dimensions of a , b and c are

m/a
`s^(3)` , m/a
`s^(2)` and m/s respectively.

Step-by-step explanation:

Velocity v of the particle varies with t and is given by

v = a
`t^(2)` + bt + c

Now, since v is the summation of a
`t^(2)` , bt and c , each of these must have the same units as of v which is m/s .

So, dimension of a
`t^(2)` should be m/s

We know that dimension of time is s , so dimension of a must be m/
`s^(3)`.

Also, dimension of bt must be m/s , while dimension of t is s,

So, dimension of b must be m/a
`s^(2)`.

Again, dimension of c must be m/s .

Thus , dimensions of a , b and c are

m/a
`s^(3)` , m/a
`s^(2)` and m/s respectively.