The cart travels the track again and now experiences a constant tangential accel

Question

The cart travels the track again and now experiences a constant tangential acceleration from point A to point C.

Learning Goal: 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. (Figure 1) The track is straight at point A and curved at points 8 and C. Correct The acceleration's direction seemingly contradicts the experiences people have inside vehicles making turns. While the vehicle is turning, its velocity is changing. Velocity is a vector; the vehicle is maintaining a constant speed, but the velocity's direction is changing. Consequently, the vehicle's occupants feel that they are being pushed in the opposite direction of the turn because, while the vehicle's velocity is changing, each of their bodies is attempting to maintain a constant velocity. The vehicle's acceleration points in the same direction as the velocity's changing direction?toward the curved path's center. Part B 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 7.10m/s at point A and 8.70mis at point C. The cart takes 5.00s to go from point A to point C, and the cart takes 1.00s 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 meters per second.

Explanation / Answer

acceleration of cart, a= (v-u)/t = (8.7-7.1)/5 = 0.32 m/s^2

time taken from A to B = 5-1 = 4 s

Velocity of cart at B, Vb = Va + at = 7.1 + 0.32(4) = 8.38 m/s

Note that, the acceleration calculated here is tangential acceleration. The centripetal acceleration or radial acceleration doesn't increase speed of the car, as it acts perpendicular to the direction of motion.

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