Question

A sports car accelerates at a rate of 8 ft/s^2 and travels 100 feet in about 2.8 seconds. What is the initial velocity to the nearest tenth?

Answer 1

To find the initial velocity of the sports car, we can use the following equation of motion:

$d=ut+\frac{1}{2}a{t}^2$

where: d is the displacement (100 ft), u is the initial velocity (unknown), a is the acceleration (8 ft/s²), and t is the time (2.8 s).

Rearranging the equation, we get:

$u=\frac{d}{t}-\frac{1}{2}a{t}^2$

Substituting the given values, we can calculate the initial velocity:

$u=\frac{100\text{ft}}{2.8\text{s}}-\frac{1}{2}\times 8{\text{ft/s}}^2\times (2.8\text{s}{)}^2$

u≈35.7143 ft/su approx 35.7143 , ext{ft/s}u<span cl