A motorcycle has a constant acceleration of 4.33 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) 40.0 to 50.0 m/s, and (b) 70.0 to 80.0 m/s?
A motorcycle has a constant acceleration of 4.33 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) 40.0 to 50.0 m/s, and (b) 70.0 to 80.0 m/s?
To solve this problem, we can use the kinematic equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
(a) For the first case, the initial velocity (u) is 40.0 m/s and the final velocity (v) is 50.0 m/s. The acceleration (a) is given as 4.33 m/s^2. We need to find the time taken (t).
Using the equation v = u + at, we can rearrange it to solve for t:
t = (v - u) / a
Plugging in the values, we have:
t = (50.0 - 40.0) / 4.33
t = 10.0 / 4.33
t ≈ 2.31 seconds
Therefore, it takes approximately 2.31 seconds for the motorcycle to change its speed from 40.0 to 50.0 m/s.
(b) For the second case, the initial velocity (u) is 70.0 m/s and the final velocity (v) is 80.0 m/s. The acceleration (a) remains the same at 4.33 m/s^2. Again, we need to find the time taken (t).
Using the same equation, we have:
t = (v - u) / a
Plugging in the values, we get:
t = (80.0 - 70.0) / 4.33
t = 10.0 / 4.33
t ≈ 2.31 seconds
Therefore, it also takes approximately 2.31 seconds for the motorcycle to change its speed from 70.0 to 80.0 m/s.
In both cases, the time taken for the motorcycle to change its speed is the same because the acceleration is constant.