Answer:
Dimensions of a , b and c are
m/a[tex]s^{3}[/tex] , m/a[tex]s^{2}[/tex] and m/s respectively.
Explanation:
Velocity v of the particle varies with t and is given by
v = a[tex]t^{2}[/tex] + bt + c
Now, since v is the summation of a[tex]t^{2}[/tex] , bt and c , each of these must have the same units as of v which is m/s .
So, dimension of a[tex]t^{2}[/tex] should be m/s
We know that dimension of time is s , so dimension of a must be m/[tex]s^{3}[/tex].
Also, dimension of bt must be m/s , while dimension of t is s,
So, dimension of b must be m/a[tex]s^{2}[/tex].
Again, dimension of c must be m/s .
Thus , dimensions of a , b and c are
m/a[tex]s^{3}[/tex] , m/a[tex]s^{2}[/tex] and m/s respectively.
