The useful equations here are derived equations for rectilinear motion at constant acceleration:
a = (v - v₀)/t
2ax = v² - v₀²
x = v₀t + 0.5at²
1. Since it starts from rest, v₀ = 0. Then, v = <span>10.5 m/s and t=1.35 s
a = (10.5 - 0)/1.35 = 7.78 m/s</span>²
a = 7.78 m/s²*(1 km/1000 m)*(3,600 s/ 1 h)² = 100,828.8 km/h²
2. v₀ = 0; v = 60 km/h; t=5.4 s
a = [60 km/h*(1000 m/1km)*(1 h/3600 s) - 0]/5.4 s = 3.09 m/s²
3. Using the acceleration and velocities in #2, we can determine the distance by the formula: 2ax = v² - v₀²
2(3.09 m/s²)x = [60 km/h*(1000 m/1km)*(1 h/3600 s)]² - (0 m/s)²
Solving for x,
x = 44.95 m
4. Using acceleration in #2 and v₀ = 0, the time would be
x = v₀t + 0.5at²
0.25 km * 1,000 m/1 km = (0)(t) + (0.5)(3.09 m/s²)(t²)
Solving for t,
t = 12.72 seconds
5. Acceleration of automobile:
a = [(55 km/h - 25 km/h)*(1,000 m/1 km)*(1 h/3,600 s)]/30 s
a = 0.278 m/s²
<span>
</span>Acceleration of bicycle:
a = [(30 km/h - 0 km/h)*(1,000 m/1 km)*(1 h/3,600 s)]/(0.5 min * 60 s/1 min)
a = 0.278 m/s²
<span>
6. x = 85 km or 85,000 m; v</span>₀ = 0 m/s; v = 2,800 m/s
2ax = v² - v₀²
2a(85,000 m) = (2,800 m/s)² - 0²
a = 46.12 m/s²
7. Using the data given and acceleration in #6,
x = v₀t + 0.5at²
85,000 m = 0*t + 0.5(46.12 m/s²)(t²)
Solving for t,
t = 60.71 seconds
Answer:
Option D
130 m
Explanation:
From the concept of speed, distance=speed*time
When traveling East, displacement=10*10=100 m (since he takes 10 seconds while traveling at a speed of 10 m/s)
When traveling West, displacement=5*6=30 m (since John takes 6 seconds to travel at a speed of 5 m/s)
Total displacement=Displacement East+ Displacement West=100+30=130 m
Answer:
The force between charges is
.
Explanation:
The Coulomb force
between the two charges
and
separated by distance
is given by the equation

where
is the coulombs constant, and has the value
.
Now in our case

and
,
therefore, the Coulomb force between the charges is


Answer:
60
Explanation:
According to the given question, the computation of minimum coating thickness is shown below:-
The condition for constructive interference is



Now we will put the values to the above formula to reach the answer

= 60
Therefore we simply applied the above formula to determine the minimum coating thickness
Explanation:
Speed of the marathon runner, v = 9.51 mi/hr
Distance covered by the runner, d = 26.220 mile
Let t is the time taken by the marathon runner. We know that the speed of the runner is given by total distance divided by total time taken. Mathematically, it is given by :



t = 2.75 hours
Since, 1 hour = 60 minutes
t = 165 minutes
Since, 1 minute = 60 seconds
t = 9900 seconds
Hence, this is the required solution.