Curvilinear Motion  Motion of projectile  Normal and tangential components

Curvilenear motion Normal and tangential components

\ v=0.12t 2 When t=0, s=0 When t=10, s=? when t = 0, v =0 → c=0 s =0.6(10 2 ) = 60 m when t = 10,

Cars traveling along a clover-leaf interchange experience an acceleration due to a change in speed as well as due to a change in direction of the velocity. If the car’s speed is increasing at a known rate as it travels along a curve, how can we determine the magnitude and direction of its total acceleration? Why would you care about the total acceleration of the car? Curvilenear motion Normal and tangential motion components

A motorcycle travels up a hill for which the path can be approximated by a function y = f(x). If the motorcycle starts from rest and increases its speed at a constant rate, how can we determine its velocity and acceleration at the top of the hill? How would you analyze the motorcycle's “flight” at the top of the hill?

ACCELERATION IN THE n-t COORDINATE SYSTEM There are two components to the acceleration vector: tangential component normal component

Constant acceleration

-tangent to the curve and in the direction of increasing or decreasing velocity. -represents the time rate of change in the magnitude of the velocity tangential components -Always directed toward the center of curvature of the curve. -represents the time rate of change in the direction of the velocity Normal/centripetal components

Magnitude of acceleration Radius of curvature

Consider these 2 cases: 1.If the particle moves along a straight line 2.If the particle moves along a curve with a constant speed

when t = 10, v =100 when t = t’, v =0 Example 2 The boxes travel along the industrial conveyor. If a box starts from rest at A and increases its speed such that a t = ( 0.2t ) m/s 2, determine the magnitude of its acceleration when it arrives at point B.

magnitude of acceleration at B; info we have; [solution]

distance from A to B; to find t B

At point B;