A motorcycle has a constant acceleration of 2.65 m/s2. Both the velocity and acceleration of the motorcycle point in the same direction. How much time is required for the motorcycle to change its speed from (a) 41.5 to 51.5 m/s, and (b) 71.5 to 81.5 m/s?
a. V = Vo + a*t
V = 51.5 m/s
Vo = 41.5 m/s
a = 2.65 m/s^2
Solve for t.
b. Same procedure and answer as part a.
To find the time required for the motorcycle to change its speed, we can use the equation:
Δv = a * Δt
Where:
Δv is the change in velocity (final velocity - initial velocity)
a is the acceleration
Δt is the change in time
Let's solve for each case:
(a) Change in speed from 41.5 m/s to 51.5 m/s:
Δv = 51.5 m/s - 41.5 m/s = 10 m/s
a = 2.65 m/s²
Plug the values into the equation:
10 m/s = 2.65 m/s² * Δt
Rearrange the equation to solve for Δt:
Δt = 10 m/s / 2.65 m/s² ≈ 3.77 s
Therefore, it takes approximately 3.77 seconds for the motorcycle to change its speed from 41.5 m/s to 51.5 m/s.
(b) Change in speed from 71.5 m/s to 81.5 m/s:
Δv = 81.5 m/s - 71.5 m/s = 10 m/s
a = 2.65 m/s²
Plug the values into the equation:
10 m/s = 2.65 m/s² * Δt
Rearrange the equation to solve for Δt:
Δt = 10 m/s / 2.65 m/s² ≈ 3.77 s
Therefore, it takes approximately 3.77 seconds for the motorcycle to change its speed from 71.5 m/s to 81.5 m/s.
Note: In both cases, the time required for the motorcycle to change its speed is the same, as the acceleration is constant.