Question

A motorcycle is moving with a velocity of 72km/h * r on a straight road. When the brakes are applied, the motorcycle comes to rest after covering a distance of 10 meters. What is its acceleration?

Answer 1

To calculate the acceleration of the motorcycle, we need to use the formula:

$v^2=u^2+2as$

where: v = final velocity (0 m/s, as the motorcycle comes to rest) u = initial velocity (72 km/h * r) a = acceleration (to be determined) s = distance covered (10 meters)

First, we need to convert the initial velocity from km/h to m/s:

Initial velocity = 72 km/h * r = 72 * 1000 * r / 3600 (converting km/h to m/s, where 1 km/h = 1000 m/3600 s)

Next, we can plug in the values into the formula:

0 = (72 * 1000 * r / 3600)^2 + 2 * a * 10

Simplifying:

0 = (20 * r)^2 + 20a

Now, we can solve this equation for acceleration (a):

400 * r^2 = -20a

a = -20 * r^2 / 400 a = -r^2 / 20

Therefore, the acceleration of the motorcycle is given by -r^2 / 20.