Question

question 18 (1 point)
the position, x, of an object is given by the equation x = a + bt + ct2, where t refers to time. what are the dimensions of a, b, and c?
distance, distance, distance
distance, time, time2
distance, distance/time, distance/ time2
distance/time, distance/ time2, distance/ time3

Explanation:

Step1: Analyze the dimension of \(x\)

Since \(x\) represents the position of an object, its dimension is distance.

Step2: Analyze the dimension of \(A\)

In the equation \(x = A+Bt + Ct^{2}\), each term must have the same dimension as \(x\). For the term \(A\), when \(t = 0\), \(x=A\). So the dimension of \(A\) is distance.

Step3: Analyze the dimension of \(B\)

For the term \(Bt\), since \(t\) has dimension of time (\(T\)) and \(Bt\) has dimension of distance (\(L\)). Let the dimension of \(B\) be \(d_{B}\). Using the formula \(L=d_{B}\times T\), we get \(d_{B}=\frac{L}{T}\) (distance/time).

Step4: Analyze the dimension of \(C\)

For the term \(Ct^{2}\), since \(t^{2}\) has dimension of \(T^{2}\) and \(Ct^{2}\) has dimension of distance (\(L\)). Let the dimension of \(C\) be \(d_{C}\). Using the formula \(L = d_{C}\times T^{2}\), we get \(d_{C}=\frac{L}{T^{2}}\) (distance/time²).

Answer:

distance, distance/time, distance/time²