0.8 1.9 kinematic equations  (Page 3/7)

Calculating displacement of an accelerating object: dragsters

Dragsters can achieve average accelerations of $\text{26}\text{.}{\text{0 m/s}}^2$ . Suppose such a dragster accelerates from rest at this rate for 5.56 s. How far does it travel in this time?

Strategy

Draw a sketch.

We are asked to find displacement, which is $x$ if we take $x_0$ to be zero. (Think about it like the starting line of a race. It can be anywhere, but we call it 0 and measure all other positions relative to it.) We can use the equation $x=x_0+v_{0}t+\frac{1}{2}{\text{at}}^2$ once we identify $v_0$ , $a$ , and $t$ from the statement of the problem.

Solution

1. Identify the knowns. Starting from rest means that $v_0=0$ , $a$ is given as $\text{26}\text{.}0{\text{m/s}}^2$ and $t$ is given as 5.56 s.

2. Plug the known values into the equation to solve for the unknown $x$ :

Since the initial position and velocity are both zero, this simplifies to

Substituting the identified values of $a$ and $t$ gives

yielding

Discussion

If we convert 402 m to miles, we find that the distance covered is very close to one quarter of a mile, the standard distance for drag racing. So the answer is reasonable. This is an impressive displacement in only 5.56 s, but top-notch dragsters can do a quarter mile in even less time than this.