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# Mechanics

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### Mechanics

1. 1.  The quantity that describes the rate of change of velocity in a given timeinterval is called acceleration. The magnitude of the average acceleration is calculated by dividing the total change in an object’s velocity by the time interval in which the change occurs.
2. 2. A shuttle bus slows down with anaverage acceleration of -1.8 m/s2.How long does it take the bus toslow from 9.0 m/s to a completestop?
3. 3. As the shuttle bus comes to asudden stop to avoid hitting a dog, itaccelerates uniformly at −4.1 m/s2as it slows from 9.0 m/s to 0.0 m/s.Find the time interval of accelerationfor the bus.
4. 4. A car traveling at 7.0 m/saccelerates uniformly at 2.5 m/s2 toreach a speed of 12.0 m/s. How longdoes it take for this acceleration tooccur?
5. 5. With an average acceleration of −1.2m/s2, how long will it take a cyclistto bring a bicycle with an initialspeed of 6.5 m/s to a completestop?
6. 6. Turner’s treadmill runs with avelocity of −1.2 m/s and speeds upat regular intervals during a half-hour workout. After 25 min, thetreadmill has a velocity of −6.5 m/s.What is the average acceleration ofthe treadmill during this period?
7. 7. Suppose a treadmill has an averageacceleration of 4.7x10−3 m/s2.a) How much does its speed changeafter 5.0 min?b) If the treadmill’s initial speed is1.7 m/s, what will its final speed be?
8. 8. When the velocity in the positive direction isincreasing, the acceleration is positive, as atpoint A. When the velocity is constant, there is noacceleration, as at point B. When the velocity inthe positive direction is decreasing, theacceleration is negative, as at point C.
9. 9. The velocity increases by exactly the sameamount during each time interval.Thus, the acceleration is constant. Becausethe velocity increases for each timeinterval, the successive change indisplacement for each time intervalincreases.
10. 10. *We know that the average velocity is equal todisplacement divided by the time interval.*For an object moving with constantacceleration, the average velocity is equal to theaverage of the initial velocity and the finalvelocity.
11. 11. We can set the expressions for average velocityequal to each other.Therefore;This is formula of displacement withconstant acceleration.
12. 12. A racing car reaches a speed of 42m/s. It then begins a uniformnegative acceleration, using itsparachute and braking system, andcomes to rest 5.5 s later. Find thedistance that the car travels duringbraking.
13. 13. A car accelerates uniformly from restto a speed of 6.6 m/s in 6.5 s. Findthe distance the car travels duringthis time.
14. 14. When Maggie applies the brakes ofher car, the car slows uniformly from15.0 m/s to 0.0 m/s in 2.50 s. Howmany meters before a stop signmust she apply her brakes in orderto stop at the sign?
15. 15. A driver in a car traveling at a speedof 21.8 m/s sees a cat 101 m awayon the road. How long will it take forthe car to accelerate uniformly to astop in exactly 99 m?
16. 16. A car enters the freeway with aspeed of 6.4 m/s and acceleratesuniformly for 3.2 km in 3.5 min.How fast (in m/s) is the car movingafter this time?
17. 17. By rearranging the equation for acceleration,we can find a value for the final velocity.Cross multiply change in t;
18. 18. Transpose initial velocity;This is formula of final velocity withconstant acceleration after t time.
19. 19. If you want to know the displacement of anobject moving with constant acceleration oversome certain time interval, you can obtainanother useful expression for displacement bysubstituting the expression for vf into theexpression for Δx.
20. 20. This is formula of displacement without vf.
21. 21. A plane starting at rest at one end ofa runway undergoes a uniformacceleration of 4.8 m/s2 for 15 sbefore takeoff. What is its speed attakeoff? How long must the runwaybe for the plane to be able to takeoff?
22. 22. A car with an initial speed of 6.5 m/saccelerates at a uniform rate of 0.92m/s2 for 3.6 s. Find the final speedand the displacement of the carduring this time.
23. 23. An automobile with an initial speedof 4.30 m/s accelerates uniformly atthe rate of 3.00 m/s2. Find the finalspeed and the displacement after5.00 s.
24. 24. A car starts from rest and travels for5.0 s with a constant acceleration of−1.5 m/s2. What is the final velocityof the car? How far does the cartravel in this time interval?
25. 25. A driver of a car traveling at 15.0m/s applies the brakes, causing auniform acceleration of −2.0 m/s2.How long does it take the car toaccelerate to a final speed of 10.0m/s? How far has the car movedduring the braking period?
26. 26. What will the final velocity be with constant acceleration after x displacement?This is formula of vf after displacement ofx with constant velocity.
27. 27. A person pushing a stroller startsfrom rest, uniformly accelerating at arate of 0.5 m/s2. What is the velocityof the stroller after it has traveled4.75 m?
28. 28. A car traveling initially at +7.0 m/saccelerates uniformly at the rate of+0.80 m/s2 for a distance of 245 m.a) What is its velocity at the end ofthe acceleration?b) What is its velocity after itaccelerates for 125 m?c) What is its velocity after itaccelerates for 67 m?
29. 29. A car accelerates uniformly in astraight line from rest at the rate of2.3 m/s2.a) What is the speed of the car afterit has traveled 55 m?b) How long does it take the car totravel 55 m?
30. 30. A motorboat accelerates uniformlyfrom a velocity of 6.5 m/s to thewest to a velocity of 1.5 m/s to thewest. If its acceleration was 2.7 m/s2to the east, how far did it travelduring the acceleration?
31. 31. An aircraft has a liftoff speed of 33m/s. What minimum constantacceleration does this require if theaircraft is to be airborne after atake-off run of 240 m?
32. 32. A certain car is capable ofaccelerating at a uniform rate of0.85 m/s2. What is the magnitude ofthe car’s displacement as itaccelerates uniformly from a speedof 83 km/h to one of 94 km/h?