Question

a truck that delivers essentials in remote areas can travel 85 kilometers.which of the following expresses the velocity v as a function of travel time t in hours? ​
a. v (t)=85/t

b v (t)=t/85
c. t (v)=85/v

d. t (v)=v/85

Answer 1

Given:

• Distance travelled by the truck to deliver essentials in remote areas =  $85kilometers$
• Velocity is dented by the letter '$v$'.
• The travel time is denoted by the letter '$t$'.

To find:

To select an option that expresses the velocity '$v$' of the truck as a function of travel time '$t$'.

To be recollected:

Function: Function is defined as the relation between each element of one set and each element of second set. Considering an example- let '$x$' be an element of one set and '$y$' be an element of another set. Now, the element   '$y$' can be expressed as a function of first set element as follows:

$y=f(x)$

Formula to be used:

The formula for calculating velocity of any body is given by:

$v=d/t$.........(1)

where, $v$ = velocity

$d$ =  distance travelled

$t$ =  time taken during travel

Solution:

• As per the given data, distance travelled by the truck = $85kilometers$

• From the given data and the equation (1), the velocity '$v$' of the truck is given by:

$v=85/t$

• From the above equation, velocity '$v$' can be expressed as a function of time '$t$' in the following way:

⇒$v(t) = 85/t$

Final Answer:

The velocity of the truck can be expressed as a function of time in the following way: $v(t)=85/t$.

∴ Option $(a)$ is correct.