Hi simple question which of these have the dimension as length?
A) a*t^2
B) v^2/2*a
C) a*v
D) (v^2*m)/F
a= m/s^2
v=m/s
t
so A is m/s^2 * s^2= m
can you do the rest?
On the last, for F, kg*m/s^2 is the units.
Still so confused @_@.
Does the dimension as length mean, when calculated the answer = length?
I would do dimensions in meters (m), using the symbols m, m/s, m/s^2 for length, velocity, acceleration. Mass is kg.
To determine which of the given expressions have the dimension of length, we need to analyze the units involved in each expression. Let's break down each option one by one:
A) a*t^2 - This expression involves the product of acceleration (a) and time squared (t^2). The unit of acceleration is typically meters per second squared (m/s^2), and the unit of time is seconds (s). Multiplying these units gives (m/s^2) * (s^2), which simplifies to meters (m). Therefore, option A has the dimension of length.
B) v^2/2*a - In this expression, v represents velocity, and a represents acceleration. The unit of velocity is typically meters per second (m/s), and the unit of acceleration is meters per second squared (m/s^2). Taking the square of velocity and dividing it by twice the acceleration yields (m/s)^2 / (2 * (m/s^2)). Simplifying this expression results in meters (m), so option B also has the dimension of length.
C) a*v - This expression is the product of acceleration (a) and velocity (v). As mentioned before, the unit of acceleration is typically meters per second squared (m/s^2), and the unit of velocity is meters per second (m/s). Multiplying these units gives (m/s^2) * (m/s), which simplifies to meters per second cubed (m/s^3). Thus, option C does not have the dimension of length.
D) (v^2*m)/F - In this expression, v represents velocity, m represents mass, and F represents force. The unit of velocity is meters per second (m/s), the unit of mass is typically kilograms (kg), and the unit of force is typically newtons (N). Squaring the velocity and multiplying it by mass, we have (m/s)^2 * kg. Dividing this expression by force, which is kg * m/s^2, results in m^3/s^2 (meters cubed per second squared). Consequently, option D does not have the dimension of length.
Therefore, options A (a*t^2) and B (v^2/2*a) have the dimension of length.