Question

A race car accelerates uniformly from 28.5 m/s to 56.1 m/s in 3.47 seconds. Determine the acceleration of the car and the distance traveled.

Answer 1

$\huge\color{orange}\boxed{\colorbox{black}{\tt{☣ANSWER☣}}}$

Initial velocity $(u)$ : 28.5 m/s

Final velocity $(v)$ : 56.1 m/s

Time taken $(t)$ : 3.47 s

Acceleration $(a)$ :

$v = u + at$

$56.1 \: m {s}^{ - 1} = 28.5 \: m {s}^{ - 1} + a(3.47 \: s)$

$56.1 \: m {s}^{ - 1} - 28.5 \: m {s}^{ - 1} = a(3.47 \: s)$

$a = \frac{27.6 \: m {s}^{ - 1} }{3.47 \: s}$

$a = 7.95 \: m {s}^{ - 2}$

Distance $(s)$ :

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

$s = 28.5 \: m {s}^{ - 1} \times 3.47 \: s + \frac{1 }{2} \times 7.95 \: m {s}^{ - 2} \times {(3.47 \: s)}^{2}$

$s = 98.9 \: m + 3.97 \: m {s}^{ - 2} \times 12.04 \: {s}^{2}$

$s = 98.9 \: m + 47.8 \: m$

$s = 146.7 \: m$