Question

A body with unknown initial velocity moves with constant acceleration. At the end of 9.15 s, it is moving at a velocity of 52.0 m/s and it is 219.0 m from where it started. Find the body's acceleration and its initial velocity.

Answer 1

Question #14201

The formulas for $S(t), v(t)$ , when object is moving with constant acceleration, are given by:

$v = v_{0} + at; S = v_{0}t + \frac{at^{2}}{2}$ . Knowing, that for $t = 9.15\mathrm{s}, v = 52\mathrm{m/s}, S = 219\mathrm{m}$ , obtain system of two equations: $52 = v_{0} + 9.15 \cdot a, 219 = 9.15 \cdot v_{0} + a \frac{(9.15)^{2}}{2}$ . Plugging the first equation, into second: $219 = (52 - 9.15a) \cdot 9.15 + \frac{a}{2}(9.15)^{2}$ , which gives $a \approx 6.13\mathrm{m/s}^{2}$ , and using first equation, $v_{0} = 52\mathrm{m/s} - 9.15s \cdot 6.13\mathrm{m/s}^{2} = -4.09\mathrm{m/s}$ .