To be able to identify the direction of the velocity and acceleration vectors du

Question

To be able to identify the direction of the velocity and acceleration vectors during curvilinear motion and to use the concept of average acceleration and velocity to solve for unknown quantities. As shown, a cart moves along a track. The track is straight at point A and curved at points B and C. If the cart moves along the track at a constant speed, what are the cart's velocity and acceleration vectors at points A, B, and C? Start your vectors at the corresponding black dots. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. The cart travels the track again and now experiences a constant tangential acceleration from point A to point C. The speeds of the cart are 12.0 ft/s at point A and 19.2 ft/s at point C. The cart takes 3.50 s to go from point A to point C, and the cart takes 1.80 s to go from point B to point C. What is the cart's speed at point B? Express your answer numerically to three significant figures in feet per second.

Explanation / Answer

Solution:

B)

As the acceleration is constant from A to C we can use kinematics equations;

V = u +at (from A to C)

=> 19.2 = 12 + a(3.5)

=> a = 2.05714 ft/s^2

As we know the time taken from A to B is : T (AB) = 3.5-1.8 = 1.7 s

Hence the speed at point B will be simply ;

V(at B) = u(at A) + a (1.7)

=> V(at B) = 19.2 + 2.05714 * 1.7

=> V(at B) = 22.697 ft/s

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