Question

If x=a+bt+ct 2 where x is in metres and t is in seconds.What is the unit of c?

Answer 1

Use the concept of dimensional analysis.

Dimension of LHS: L

According to concept of dimensional analysis, dimension of each term of LHS is equal to that of each term of RHS.

So, Dimension of x = Dimension of Ct^2

L = [C]T^2

Therefore,

[C] =LT^-2

So unit of C is m/s^2.

Answer 2

If x = a + bt + ct² , where x is in meter and t is in second.

We have to find the unit of c.

from the fundamental concept of units,

• if two or more quantites are in addition or subtraction, their units must be the same. for example, a = b ± c , here unit of a = unit of b = unit of c.
• if two or more quantities are in multiplication, we can apply the product of unit of each of them. for example, x = pq , here unit of x = unit of p × unit of q.

we have to find the unit of c, but we see, c is multiplied with t².

∴ unit of x = unit of ct²

⇒ unit of x = unit of c × unit of t²

given,

the unit of x = meter

and the unit of t = second

∴ meter = unit of c × (second)²

⇒ unit of c = meter/second² = m/s²

Therefore the unit of c is as same as that of acceleration and that is m/s².