Question

the rate of change of velocity, v, with time (change in time), t, is called acceleration, a. acceleration is given by the equation ( a=\frac{v}{t} ). which of the following expression represents the change in time, t, within which the acceleration, a, occurs?
a ( t = va )
b ( t = a - v )
c ( t=\frac{a}{v} )
d ( t=\frac{v}{a} )
e ( t = a + v )

Explanation:

Step1: Isolate \( t \)

Given \( a=\frac{v}{t} \), multiply both sides by \( t \).
\( a\times t=\frac{v}{t}\times t \)
\( at = v \)

Step2: Solve for \( t \)

Divide both sides by \( a \).
\( t=\frac{v}{a} \)

Answer:

D. \( t=\frac{v}{a} \)