When moving at highway speed, a Triumph America motorcycle is capable of accelerating at 2.1 m/s2. At this rate, how long does it take to accelerate from 103 km/h to 88 km/h?
To determine the time it takes to accelerate from 103 km/h to 88 km/h, we need to first convert these speeds to meters per second (m/s) because the acceleration is given in m/s^2.
To convert from km/h to m/s, we can use the following conversion factor:
1 km/h = 1000 m/3600 s = 10/36 m/s
So, the initial velocity (u) of 103 km/h can be converted to m/s as follows:
u = 103 km/h * (10/36 m/s per 1 km/h) = 28.6 m/s (approximately)
Similarly, the final velocity (v) of 88 km/h can be converted to m/s as follows:
v = 88 km/h * (10/36 m/s per 1 km/h) = 24.4 m/s (approximately)
Now, we can use the following formula of motion to find the time (t):
v = u + at
Here, u is the initial velocity (28.6 m/s), v is the final velocity (24.4 m/s), and a is the acceleration (2.1 m/s^2). We need to solve for t.
Rearranging the formula, we have:
t = (v - u) / a
Substituting the given values, we get:
t = (24.4 m/s - 28.6 m/s) / 2.1 m/s^2
Calculating this, we find:
t = (-4.2 m/s) / 2.1 m/s^2 = -2 s (approximately)
The negative sign indicates that the acceleration is opposite to the direction of motion. However, time cannot be negative in this context. Therefore, we can conclude that there is an error in the given values or the question itself.