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

Dimensions of a , b and c are

m/a  , m/a and m/s respectively.

Explanation:

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

v = a + bt + c

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

So, dimension of a should be m/s

We know that dimension of time is s , so dimension of a must be m/.

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

So, dimension of b must be m/a.

Again, dimension of c must be m/s .

Thus , dimensions of a , b and c are

m/a  , m/a and m/s respectively.

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