A motorcycle has a constant acceleration of 2.13 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) 24.0 to 34.0 m/s, and (b) 54.0 to 64.0 m/s
Divide the speed change (10 m/s) by the acceleration rate.
Both answers should be the same.
To find the time required for the motorcycle to change its speed, we can use the formula:
time = (final velocity - initial velocity) / acceleration
(a) Given:
Initial velocity (u) = 24.0 m/s
Final velocity (v) = 34.0 m/s
Acceleration (a) = 2.13 m/s²
Substitute the given values into the formula:
time = (34.0 - 24.0) / 2.13
Calculating the value inside the parenthesis:
time = 10.0 / 2.13
Divide 10.0 by 2.13 to find the time:
time ≈ 4.69 seconds
Therefore, it takes approximately 4.69 seconds for the motorcycle to change its speed from 24.0 to 34.0 m/s.
(b) Given:
Initial velocity (u) = 54.0 m/s
Final velocity (v) = 64.0 m/s
Acceleration (a) = 2.13 m/s²
Substitute the given values into the formula:
time = (64.0 - 54.0) / 2.13
Calculating the value inside the parenthesis:
time = 10.0 / 2.13
Divide 10.0 by 2.13 to find the time:
time ≈ 4.69 seconds
Therefore, it takes approximately 4.69 seconds for the motorcycle to change its speed from 54.0 to 64.0 m/s.
In both cases, the time required for the motorcycle to change its speed is approximately 4.69 seconds.