Motion in a straight line and a cyclist

In summary, the cyclist rode for 40 seconds and travelled 250 meters before reaching the hill and then traveled another 200 meters beyond the hill. The car passed the truck 312.5 meters past the starting point after traveling at a speed of 50 meters per second.
  • #1
Mary1910
31
1
Could someone please check my work? Thanks :)

A cyclist rode east for 1.0 x 10^2 m with a constant velocity of 25.0m/s. She then accelerated down a hill, and 5.0s later reached the bottom of the hill with a velocity of 50.0m/s.

a)How long did the cyclist ride before reaching the hill?

time=distance/velocity

t=1000m / 25m/s
=40sb)What was her average acceleration down the hill?

acceleration=change in velocity/time

a=50m/s-25m/s / 5s
=25m/s / 5s
=10m/s^2c)What was the distance she traveled down the hill?

distance=velocity x time

d=(50.0m/s)(5s)
=250md)If she continued to ride a constant velocity for another 5.0s, how far beyond the hill would she travel?

distance=velocity x time

d=(50.0m/s)(5s)
=250mAt the instant a traffic light turns green, a car starts from rest and accelerates uniformly at a rate of 4.0m/s (E). At the same instant, a truck traveling with a constant velocity of 90.0km/h (E) overtakes and passes the car.

a)How far beyond the starting point is the car after 10.0s?

delta d= (v1)(delta t) + 1/2 (a)(delta t^2)
=(0)(10)+1/2(4.0m/s)(100)
=200m

b)How far beyond the starting point is the truck after 10.0s?

distance=velocity x time
=(90km/h)(10.0s)
=(25m/s)(10.0s)
=250m

c)The car passes the truck at a distance of 312.5m beyond the starting point. How fast is the car traveling at this instant?

v2^2=v1^2 + 2(a)(delta d)
=0+2(4.0m/s)(312.5m)
=2500m/s^2
=50m/s

d)How long does the car take to pass the truck?

delta t=v2-v1/a
=50m/s-0m/s / 4.0m/s
=12.5s

e)Both drivers suddenly see a barrier 100.0m away and hit their brakes at exactly the same time. Assuming that both vehicles decelerate uniformly, and they take 3.0s to stop, will they stop in time?

Car
delta d=1/2(v1+v2)delta t
=1/2(50m/s)(3.0s)
=75m

Truck
delta d=1/2(v1+v2)delta t
=1/2(90km/h)(3.0s)
=1/2(25m/s)(3.0s)
=37.5s

Therefore both the car and the truck will be able to stop in time.Thank you so much to anyone took the time to look over this and give feedback!

-Mary
 
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  • #2
You have used a plug-and-chug style, which can trip you up when you pick the wrong equations - i.e. in part (c).
d=v/t only owrks for a constant velocity. While the cyclist was on the hill, she was accelerating.

The trick with these problems is to sketch the velocity-time graph.
The displacement is the area under the relevant section of the graph, the acceleration is the slope - that's usually easier than remembering the equations.
 
  • #3
Thank you
 
  • #4
No worries - how did you get on?
 
  • #5


Your calculations and responses seem to be correct and well-explained. Good job on using the appropriate equations and units. However, for part e) it seems like you may have made a typo in the calculation for the truck's stopping distance. It should be 1/2(25m/s)(3.0s) = 37.5m, not 37.5s. Other than that, great work!
 

1. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of both the speed and direction of an object's motion. In other words, velocity takes into account the direction of an object's movement, while speed does not.

2. How is acceleration related to motion in a straight line?

Acceleration is the rate of change of velocity, which means it measures how much an object's velocity changes over time. In motion in a straight line, acceleration can be caused by changes in speed or changes in direction.

3. How does a cyclist maintain a constant velocity?

A cyclist can maintain a constant velocity by balancing the forces acting on them. In motion in a straight line, a cyclist can maintain a constant velocity by pedaling at a constant speed and ensuring that the net force acting on them is zero.

4. What factors affect a cyclist's speed and velocity?

The speed and velocity of a cyclist are affected by factors such as the grade of the road, the cyclist's physical abilities, the type of bicycle, and external forces such as air resistance and friction.

5. How does a cyclist's motion in a straight line change when going uphill versus downhill?

When going uphill, a cyclist's motion in a straight line will have a greater acceleration due to the increased force of gravity pulling them back. On the other hand, when going downhill, a cyclist's motion in a straight line may have a constant velocity or even decelerate due to the opposing force of friction.

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