Help on Unit Question. During a short interval of time the speed v in m/s of an automobile is given by...?

Question

During a short interval of time the speed v in m/s of an automobile is given by v = at^2 + bt^3, where the time t is in seconds. The units of a and b are respectively:

a.) m x s^2; m x s^4

b.) s^3/m; s^4/m

c.) m/s^2; m/s^3

d.) m/s^3; m/s^4

e.) m/s^4; m/s^5

An answer and explanation would be greatly appreciated. Thanks :)

Answer 1

Ans (d)

Explanation: v is in m/s

Therefore, each term in the expression for v is in m/s

Therefore, at^2 is in m/s

t^2 is in s^2 (because t is in s)

a = at^2/t^2

Therefore, a is in (m/s)/s^2 = m/s^3

bt^3 is in m/s

t^3 is in s^3

b = bt^3/t^3

Therefore, b is in (m/s)/s^3 = m/s^4