Studdy AI Logo
Math  /  Algebra

QuestionA motorcyclist being monitored by radar accelerates at a constant rate from 0mph(v(0)=0)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

STEP 1

1. The motorcyclist accelerates at a constant rate.
2. The initial velocity v(0)=0 v(0) = 0 mph.
3. The final velocity v(18)=50 v(18) = 50 mph.
4. Time duration is 18 seconds.
5. We need to convert seconds to hours for consistency in units.
6. We are to find the distance traveled in miles.

STEP 2

1. Convert time from seconds to hours.
2. Calculate the acceleration.
3. Use the kinematic equation to find the distance traveled.

STEP 3

Convert time from seconds to hours.
Since there are 3600 seconds in an hour, we convert 18 seconds to hours:
Time in hours=183600=1200 hours \text{Time in hours} = \frac{18}{3600} = \frac{1}{200} \text{ hours}

STEP 4

Calculate the acceleration.
The acceleration a a can be calculated using the formula:
a=ΔvΔt=v(18)−v(0)Δt a = \frac{\Delta v}{\Delta t} = \frac{v(18) - v(0)}{\Delta t}
Substitute the known values:
a=50 mph−0 mph1200 hours=50×200=10000 mph2 a = \frac{50 \text{ mph} - 0 \text{ mph}}{\frac{1}{200} \text{ hours}} = 50 \times 200 = 10000 \text{ mph}^2

STEP 5

Use the kinematic equation to find the distance traveled.
The distance d d traveled under constant acceleration can be found using the equation:
d=v0⋅t+12at2 d = v_0 \cdot t + \frac{1}{2} a t^2
Substitute the known values:
d=0⋅1200+12×10000×(1200)2 d = 0 \cdot \frac{1}{200} + \frac{1}{2} \times 10000 \times \left(\frac{1}{200}\right)^2
d=12×10000×140000 d = \frac{1}{2} \times 10000 \times \frac{1}{40000}
d=1000080000 d = \frac{10000}{80000}
d=18 miles d = \frac{1}{8} \text{ miles}
After 18 seconds, the motorcycle has traveled 18 \boxed{\frac{1}{8}} miles.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord