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ange View Share Window Help Assignment05 Add Page Insert Table Chart Text Shape Media Comment starting position (not counting when t 0 s)? A cyclist maintains a constant velocity (in the positive direction) of 15 m/s along a flat portion of road for 30 seconds, then hits a downhill portion where they accelerate at 1 m/s2 for 3 seconds. How long (in m) is the downhill portion of the road? 5. 6. How far (in m) did the cyclist in the previous problem travel during the 33 second interval? 7. If the cyclist from the previous problems applies the brakes and uniformly (constant acceleration) slows to a stop, taking up a distance of 45 m, how long (in s) does it take for them to stop? 8. What acceleration (in m/s2) is required for the cyclist to stop as described? 9. A roller coaster car starts down a hill from rest. While on the hill, it accelerates uniformly. If the trip down the hill takes 6.0 s, and the hill is 45.0 m long, how fast (in m/s) is the roller coaster car going at the bottom of the hill?

Explanation / Answer

5) the length of the downhill portion, d2 = u*t2 + (1/2)*a*t2^2

= 15*3 + (1/2)*1*3^2

= 49.5 m

6) d = d1 + d2

= vo*t1 + d2

= 15*30 + 49.5

= 499.5 m

7) let a is the acceleration and t is the time taken

use, v^2 - u^2 = 2*a*s

0^2 - 15^2 = 2*a*45

==> a = -15^2/(2*45)

= -2.5 m/s^2

now use, v = u + a*t

t = (v - u)/a

= (0 - 15)/(-2.5)

= 6 s

8) a = -2.5 m/s^2

9) let a is the accaleration

use, s = u*t + (1/2)*a*t^2

45 = 0 + (1/2)*a*6^2

==> a = 2*45/6^2

= 2.5 m/s^2

now use, v = u + a*t

= 0 + 2.5*6

= 15 m/s

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