High School

A motorcycle has a constant acceleration of [tex]3.20 \, \text{m/s}^2[/tex]. Both the velocity and acceleration of the motorcycle point in the same direction.

(a) How much time is required for the motorcycle to change its speed from 19.1 m/s to 29.1 m/s?

(b) How much time is required for the motorcycle to change its speed from 49.1 m/s to 59.1 m/s?

Answer :

The time required for the motorcycle to change its speed from 19.1 m/s to 29.1 m/s is approximately 3.125 seconds and time required for the motorcycle to change its speed from 49.1 m/s to 59.1 m/s is approximately 3.125 seconds.

Given:

Constant acceleration of the motorcycle, a = 3.2 m/s²

Final velocity of motorcycle in case (a), v₂ = 29.1 m/s

Initial velocity of motorcycle in case (a), v₁ = 19.1 m/s

Final velocity of motorcycle in case (b), v₂ = 59.1 m/s

Initial velocity of motorcycle in case (b), v₁ = 49.1 m/s

Time required to change speed, t

To find: Time required to change speed

Using the formula for motion with constant acceleration:

v₂ = v₁ + at

Rearranging the equation, we get:

t = (v₂ - v₁) / a

For case (a):

Substituting the given values, we get:

t = (29.1 - 19.1) / 3.2

t ≈ 3.125 seconds

For case (b):

Substituting the given values, we get:

t = (59.1 - 49.1) / 3.2

t ≈ 3.125 seconds

The time required for the motorcycle to change its speed from 19.1 m/s to 29.1 m/s is approximately 3.125 seconds.

The time required for the motorcycle to change its speed from 49.1 m/s to 59.1 m/s is approximately 3.125 seconds.

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