The dimension of a/b where x is the distance and t is the time is T
Given the expression
x = at + bt²
where
x is the distance
t is the time
Based on the homogeneity principle, the expression on the left-hand side must be equal to that on the right. Hence;
x = at
Since x is the distance and distance is measured in metres, the dimension equivalent will be the length 'L'
Since t is the time and time is measured in seconds, the dimension equivalent will be the seconds 'T'
Similarly;
x = bt²
Next is to get a/b;
Hence the dimension of a/b is T
As per Newton's II law we know that
here we know that
now the mass of the object will be given as
so mass of the object will be 13.3 kg
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Answer:
0.82 m/s
Explanation:
From the law of conservation of momentum,
Total momentum = Final momentum.
mu+m'u' = V(m+m')......................... equation 1
Where m = mass of Lillian, u = initial velocity of Lillian before she catches the dog, m' = mass of the dog, u' = initial velocity of the dog, V = velocity of Lillian and the dog.
make V the subject of the equation,
V = (mu+m'u')/(m+m')................ Equation 2
Given: m = 40 kg, m' = 15 kg, u = 0 m/s (Lillian was standing at rest), u' = 3.0 m/s.
Substitute into equation 2
V = (40×0+15×3)/(40+15)
V = (0+45)/55
V = 45/55
V = 0.82 m/s
