Question

If x=at+bt2 where x is the distance travelled by the body in kilometers while t is the time in seconds,then the unit of b is

Answer 1

uni of b is m/s^2 same as that of acceleration

Answer 2

Answer:

The dimension of b is km/s²  or  1000 m/s²

Explanation:

Given that,

$x = at+bt^2$

We know that,

In case of addition all terms must be dimensional equal.

Therefore,

Dimension of x = Dimension of at = Dimension of bt²

Here, we need to find the dimension of b

We are given the x is the distance travelled by the body in kilometers.

So, Dimension of bt² is kilometers

t is the times in seconds

b (second)² = kilometer

b = kilometer / second²

1 kilometer = 1000 m

Hence, The dimension of b is km/s²  or  1000 m/s²