# College Physics Problem 2.30

#### A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m.(a) How long did the acceleration last? (b) Calculate the acceleration.

SOLUTION:

Given:
$v_0=0$
$v=65\:m/s$
$\Delta x=0.250\:m$

Part b and a
Solve for the acceleration first using the formula

$v^2=v_0^2+2a\Delta x$

Substitute the given values
$\left(65.0\:m/s\right)^2=\left(0\right)^2+2a\left(0.250\:m\right)$
$a=\frac{\left(65.0\:m/s\right)^2}{2\left(0.250\:m\right)}$
$a=8450\:m/s^2$

Substitute this value of acceleration to the formula $a=\frac{v-v_0}{t}$  to solve for time.

$8450\:m/s^2=\frac{65.0\:m/s-0}{t}$
$t=\frac{65.0\:m/s^2}{8450\:m/s^2}$
$t=\frac{1}{130}\:s\:\approx 7.6923\times 10^{-3}\:s$

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