Question

How long did the acceleration last for a fireworks shell accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m?

a) 0.23 s
b) 0.34 s
c) 0.45 s
d) 0.56 s

Answer 1

The acceleration of the fireworks shell can be found using the formula a = v^2 / (2d), where a is the acceleration, v is the final velocity, and d is the distance. The time it took for the acceleration to occur can be found using the formula t = sqrt(2d/a). In this case, the acceleration lasted approximately 0.003 seconds. The correct option is a) 0.23 s.

Step-by-step explanation:

To find the time it took for the fireworks shell to accelerate, we can use the formula:

t = sqrt(2d/a)

where t is the time, d is the distance, and a is the acceleration.

Using the given values, we have:

t = sqrt(2 * 0.250 m / a)

To calculate the acceleration, we can use the formula:

a = v^2 / (2d)

where v is the final velocity and d is the distance.

Using the given values, we have:

a = (65.0 m/s)^2 / (2 * 0.250 m)

Calculating the acceleration gives us:

a = 845.0 m/s^2

Plugging this value into the equation for time, we have:

t = sqrt(2 * 0.250 m / 845.0 m/s^2)

Calculating the time gives us:

t ≈ 0.003 s

Therefore, the acceleration lasted approximately 0.003 seconds.

The correct option is a) 0.23 s.