If a truck travels 100 miles in 2 hours, what is its speed?
2 answers:
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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
a) 10 m/s
b) 25 m
Explanation:
a)
The body is moving with a constant acceleration, therefore we can solve the problem by using the following suvat equation:
where
u is the initial velocity
v is the final velocity
a is the acceleration
t is the time
For the body in this problem:
u = 0 (the body starts from rest)
is the acceleration
t = 5 s is the time
So, the final velocity is
b)
In this second part, we want to calculate the distance travelled by the body.
We can do it by using another suvat equation:
where
u is the initial velocity
v is the final velocity
a is the acceleration
s is the distance travelled
Here we have
u = 0 (the body starts from rest)
is the acceleration
v = 10 m/s is the final velocity
Solving for s,