Answer:
8450 m/s²
Step-by-step explanation:
To calculate the time it took for the fireworks shell to accelerate from rest to a velocity of 65.0 m/s over a distance of 0.250 m, we can use the formula:
[ t = \frac{{v_f - v_0}}{{a}} ]
Where:
( t ) is the time of acceleration,
( v_f ) is the final velocity (65.0 m/s),
( v_0 ) is the initial velocity (0 m/s), and
( a ) is the acceleration.
First, let’s calculate the acceleration using the formula:
[ a = \frac{{v_f^2 - v_0^2}}{{2 \cdot \Delta x}} ]
Substituting the given values, we have:
[ a = \frac{{(65.0 , \text{{m/s}})^2 - (0 , \text{{m/s}})^2}}{{2 \cdot 0.250 , \text{{m}}}} ]
Simplifying this expression gives us an acceleration of 8450 m/s²