A child trying to catch an ice-cream truck (kinematics question)

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In summary, the child is running at a maximum speed of 4.0 m/s to catch an ice-cream truck that is stopped at the side of the road. However, when the child is 20 m away, the truck starts to accelerate at a rate of 1.0 m/s^2. Using the equations d = vt and d = v1t + 1/2at^2 + 20, it is determined that the child does not catch the truck as there is no real solution for t. This is also confirmed by finding out how far apart they are when the truck reaches 4 m/s.
  • #1
Sean1218
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Homework Statement



A child is running at her maximum speed of 4.0 m/s to catch an ice-cream truck, which is stopped at the side of the road. When the child is 20 m from the truck, the ice-cream truck starts to accelerate away at a rate of 1.0 m/s^2. Does the child catch the truck?


Homework Equations



d = vt
d = v1t + 1/2at^2 + 20

The Attempt at a Solution



4t = 1/2(1)t^2 + 20
0 = 1/2t^2 - 4t + 20

I can't factor normally, and I get error (square root of negative number) when I use quadratic equation. What is this telling me? That the child doesn't catch the ice-cream truck? Why? or did I do something wrong?
 
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  • #2
There's no real solution to t: so the child never catches up. You're right. Another way to think about this is to find out how far apart they are when the ice-cream truck hits 4 m/s (if the child hasn't caught up at this stage, then she'll never catch up).
 
  • #3
you have done the sum right! :smile:
Your negative square root indicates the child doesn't reach the truck...poor guy, i pity him:biggrin:
 

Related to A child trying to catch an ice-cream truck (kinematics question)

1. How long will it take for the child to catch the ice-cream truck?

The time it takes for the child to catch the ice-cream truck depends on the distance between the child and the truck, as well as the speed of the truck. The child's own speed and agility also play a role in determining the time it takes to catch the truck.

2. What is the acceleration of the child when trying to catch the ice-cream truck?

The acceleration of the child can be calculated by dividing the change in velocity by the time it takes to catch the truck. This will give the average acceleration of the child during the time period. Factors such as the child's physical abilities and the terrain may affect the acceleration.

3. How does the speed of the ice-cream truck affect the child's chances of catching it?

The speed of the ice-cream truck plays a significant role in the child's chances of catching it. If the truck is moving at a high speed, the child will have to run faster and cover more distance in a shorter period of time, making it more challenging to catch the truck. On the other hand, if the truck is moving at a slower speed, the child may have a better chance of catching it.

4. What factors can affect the child's ability to catch the ice-cream truck?

There are several factors that can affect the child's ability to catch the ice-cream truck. These include the child's speed, agility, and physical fitness, as well as the speed and distance of the truck. The terrain and any obstacles in the way can also impact the child's ability to catch the truck.

5. Can the child catch the ice-cream truck if it is moving at a constant speed?

Yes, the child can catch the ice-cream truck even if it is moving at a constant speed. However, the child will have to run at a faster speed than the truck in order to catch up to it. If the child's speed is not fast enough, they will not be able to catch the truck.

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