Question

A car moved at a constant rate along a straight line. Deepak recorded in the chart below the car's distance $\left(x\right)$, in feet, from a reference point at the start of the experiment and for each of $5$ times $\left(t\right)$ , in seconds.

t	0	1	2	3	4	5
x	10	14	18	22	26	30

Which of the following equations represents this data?

• A. $x=t+10$
• B. $x=4t+6$
• C. $x=4t+10$
• D. $x=10t+4$
• E. $x=14t$

Answer 1

The correct option is C $x=4t+10$

Observe that in the following series, $d$ follows an Arithmetic progression with $t$ being the term number.

Hence, $x_n=x_0+(t-1)\left(r\right)$ where $r$ is the common difference.

Now $r=14-10=18-14=22-18=4$ and $x_0=10$.

Therefore $x_n=10+4\left(\right(t+1)-1)$ since at $t=0,x=10$ or $d=10+4t$