# Problem: 1. An object moves clockwise with decreasing speed around an oval track. The velocity vectors at points G and H are shown. a. In the space at right, copy the velocity vectors  and . From these vectors, determine the change in velocity vector, .b. If point H were chosen to lie closer to point G, describe how  would change (direction and magnitude). c. Describe how you would determine the acceleration (direction and magnitude) at point G. In the space at right, indicate the direction of the acceleration of the object at point G. d. Copy  and  (placed "tail-to-tail") in the space at right. How does the angle between the acceleration and velocity vectors compare to 90°? (i.e., Is the angle greater than, less than, or equal to 90°?) e. Generalize your results above and from tutorial to answer the following question: For an object moving along a curved trajectory, how does the angle between the acceleration and velocity vectors compare to 90° if the object moves with (i) constant speed, (ii) increasing speed, and (in) decreasing speed?

###### FREE Expert Solution

a.

The resultant vector, Δv, from vectors, vG and vH is,

$\mathbf{∆}\stackrel{\mathbf{⇀}}{\mathbf{v}}\mathbf{=}{\stackrel{\mathbf{⇀}}{\mathbf{v}}}_{\mathbf{H}}\mathbf{-}{\stackrel{\mathbf{⇀}}{\mathbf{v}}}_{\mathbf{G}}$

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###### Problem Details

1. An object moves clockwise with decreasing speed around an oval track. The velocity vectors at points G and H are shown.

a. In the space at right, copy the velocity vectors  and . From these vectors, determine the change in velocity vector, .

b. If point H were chosen to lie closer to point G, describe how  would change (direction and magnitude).

c. Describe how you would determine the acceleration (direction and magnitude) at point G. In the space at right, indicate the direction of the acceleration of the object at point G.

d. Copy  and  (placed "tail-to-tail") in the space at right. How does the angle between the acceleration and velocity vectors compare to 90°? (i.e., Is the angle greater than, less than, or equal to 90°?)

e. Generalize your results above and from tutorial to answer the following question:

For an object moving along a curved trajectory, how does the angle between the acceleration and velocity vectors compare to 90° if the object moves with (i) constant speed, (ii) increasing speed, and (in) decreasing speed?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Centripetal Forces & Curves concept. If you need more Centripetal Forces & Curves practice, you can also practice Centripetal Forces & Curves practice problems.

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Based on our data, we think this problem is relevant for Professor Dubson's class at UCB.