QuestionA motorcyclist being monitored by radar accelerates at a constant rate from $0 \mathrm{mph}(\mathrm{v}(0)=0)$ to 50 mph in 18 sec . How far has the motorcycle traveled after 18 sec? (Hint: Convert seconds to hours.)
After 18 sec , the motorcycle has traveled $\square$ mi. (Simplify your answer. Type an integer or a fraction.)

Studdy Solution
Use the kinematic equation to find the distance traveled.
The distance $d$ traveled under constant acceleration can be found using the equation:
$$d = v_0 \cdot t + \frac{1}{2} a t^2$$
Substitute the known values:
$$d = 0 \cdot \frac{1}{200} + \frac{1}{2} \times 10000 \times \left(\frac{1}{200}\right)^2$$
$$d = \frac{1}{2} \times 10000 \times \frac{1}{40000}$$
$$d = \frac{10000}{80000}$$
$$d = \frac{1}{8} \text{ miles}$$
After 18 seconds, the motorcycle has traveled $\boxed{\frac{1}{8}}$ miles.