Question : A body of mass m accelerates uniformly from rest to velocity v1 in time t1. Find the expression for instantaneous power delivered to the body as a function of time t.
Doubt by Zoha
Solution :
mass of the body = m
initial velocity (u) = 0
final velocity (v) = v1
final velocity (v) = v1
time taken (t) = t1
Using 1st Equation of Motion
v=u+at
v1=0+a(t1)
v1=at1
a=v1/t1 — (1)
Force exerted on the body of mass m
F = ma
F = m(v1/t1) [from equation (1)] — (2)
F = ma
F = m(v1/t1) [from equation (1)] — (2)
Velocity acquired by the body in time t
v=u+at
V=0+at
V=at
V=0+at
V=at
V=(v1/t1)t [from equation 1]
V=(v1/t1)t— (3)
Powered Delivered (P) = FV
P = m(v1/t1)×(v1/t1)t [From equation 2 and 3]
P = mv1²t/t1²
P = m(v1/t1)×(v1/t1)t [From equation 2 and 3]
P = mv1²t/t1²