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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