Question

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

a) (a) 845 m/s²; (b) 0.14 s
b) (a) 650 m/s²; (b) 0.25 s
c) (a) 260 m/s²; (b) 1.25 s
d) (a) 520 m/s²; (b) 0.50 s

Answer 1

The acceleration of the fireworks shell is 260 m/s², and the time taken for the acceleration can be found by solving a quadratic equation.

Step-by-step explanation:

To calculate the acceleration of the fireworks shell, we can use the equation:

acceleration = (final velocity - initial velocity) / time

Since the initial velocity is 0 m/s and the final velocity is 65.0 m/s, and the distance traveled is 0.250 m, we can rearrange the equation to solve for acceleration:

acceleration = (65.0 m/s - 0 m/s) / 0.250 m = 260 m/s²

To calculate the time taken for the acceleration, we can use the equation:

distance = (initial velocity * time) + (1/2 * acceleration * time^2)

Since the initial velocity is 0 m/s and the distance traveled is 0.250 m, we can rearrange the equation to solve for time:

0.250 m = (0 * time) + (1/2 * 260 m/s² * time^2)

Simplifying this equation gives us a quadratic equation, which we can solve to find the time.