If the unit of velocity is 4ms and the unit of acceleration is 24ms and the unit of force is 6n
Answers
Answer:
The dimension of power is Nm/s or watts the SI unit for power. Now integrate power with respect to time you get energy which is expressed in Watt-seconds or Joules, the SI unit of energy.
Some have responded saying 4J.
We cannot directly use dimensional approach in all cases. In this case it gives us 4 joules as energy which is wrong!
Why?
Because , the question involving energy should give a clear indication of the time over which energy should be calculated. here if its like an object which started with 0m/s to 4m/s with a Force of 6N creating an acceleration of 24m/s/s. then you could do two things.
find the mass and calculate the kinetic energy.
K.E (kinetic energy ) = 0.5*mass*velocity^2 which here means
0.5 * (6/24) * 4*4 = 2J of energy.
Another way is that you calculate the time needed to go from 0m/s to 4m/s which is given by V=u+a*t. u is initial velocity (0m/s), V=4m/s and t is unknown.
rearranging this you will get time = 1/6 th of a second.
now we know the power is Force * Velocity. so now we know the instantaneous power at start ( 6N * 0m/s = 0 Watts ). At final point it is 6N*4m/s = 24W.
one would be so tempted to do power*time which is so wrong because it is not just power * time but an integration of power over time. so, seeing the below graph we should calculate the “area under the curve” which is 0.5*24*(1/6 ) (area of a right angled triangle) = 2 J

Dimensional approach is a very nice method to solve problems but they have a major problem as they cannot say whether constants are involved in your equations. So, use dimensional approach with a pinch of salt.