Answer:
B. LT⁻¹
Explanation:
The question is incomplete. Here is the complete question,
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .
Since velocity is the rate of change of displacement of a body, then;
VELOCITY = DISPLACEMENT/TIME
displacement is measured in metres while time in seconds.
expressing the formula in terms of its fundamental unit,
v = metre/secs
Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;
V = L/T
V = L * 1/T
V = L * T⁻¹
V = LT⁻¹
Hence the dimension of b is LT⁻¹.
Note that the dimension of a body is written in terms of its fundamental quantities.