Question

A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the
x axis be parallel to the ground and +y axis point upward. In the time interval from t=0 to t=4 s the trajectory of the caralong a certain section of the track is given by
→r=A(1 m/s)t^i+A((1 m/s3)t3−6(1 m/s2)t2)^j, where A is positive dimensionless constant.a. At t=2.0s is the roller coaster car ascending or descending?
b. Derive a general expression for the speed v of the car. Make sure that your expression would give the correct value for the speed (in m/s), but you don't need to put in anything explicitly about units (unlike what you see in the original expressionfor →r. Express your answer in meters per second in terms of A and t.

Answer 1

Answer:

Explanation:

r=A(1 m/s)t^i+A((1 m/s3)t3−6(1 m/s2)t2)^j,

dr / dt = A i  + (3 A t² - 6 x 2 t ) j

At t = 2

dr / dt = A i  + (12A - 24 A ) j  = A i - 12 A j .

Since slope is negative so velocity is downwards , hence it is descending

b ) velocity = dr / dr =  .  A i  + (3 A t² - 6 x 2 t ) j

Vx = A

Vy = 3A t² - 12 t