Question

During a short interval of time the speed V in m/s of an automobile is given by v = at2 + bt3 where the time T is in seconds the units of A and B are respectively:

Answer 1

Answer:

Explanation:

v is velocity, so it has to have units of m/s. In a physical equation, the units of the left side have to be the same as the units on the right side, so at2 + bt3 also has to have units of m/s. Adding things together doesn't change their units, so at2 and bt3 each have to have the units m/s.

So what you are really doing is asking "what units does a have to have so that when I multiply it by t2 I end up with m/s?" t has the unit s, so t2 is s2. So the equation you are solving is m/s=a*s2. Work that out and you can see that a has to have units of m/s3 . Proceed similarly to find the units of b.

Answer 2

Answer:

Dimension of a is [L][T]⁻³ and Dimension of b is [L][T]⁻⁴ .

Explanation:

Given that :

• v = at² + bt³
• Dimension of v = [L][T]⁻¹

Solution :

• From the Principle of Homogeneity of Dimension, " For an equation to have any physical meaning, the terms combining the equation must have the same dimensions.
• Dimension of v = Dimension of at²
• [L][T]⁻¹ = a[T]²
• a = [L][T]⁻³ = m/sec³

• Similarly, Dimension of v = Dimension of bt³
• [L][T]⁻¹ = b[T]³
• b = [L][T]⁻⁴ = m/sec⁴
• Hence, dimension of a is [L][T]⁻³ and dimension of b is [L][T]⁻⁴ .