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 the positive y axis point upward. In the time interval from t=0 to t=4 s, the trajectory of the car along a certain section of the track is given by

r⃗ =A(1m/s)ti^+A[(1m/s3)t3−6(1m/s2)t2] j^,
where A is a positive dimensionless constant.
A. At t=2.0s is the roller coaster car ascending or descending?
At is the roller coaster car ascending or descending?
ascendingdescendingB. 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 expression for r⃗ ).
Express your answer in meters per second in terms of A and t.
v = m/s
C. The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding 20m/s. Find the maximum value of A allowed by these regulations.
Express your answer using two significant figures


the maximum allowable speed value in a roller coaster is given as

v = 20 m / s

now from kinematics we can say

v ^ 2 - v_i ^ 2 = 2 as

here will be the initial speed

v_i = 0

acceleration is due to gravity

a = 9.8 m / s ^ 2

now we can use this to get the height

20 ^ 2 - 0 ^ 2 = 2 * 9.8 * h

400 = 19.6 * h

h = 20.4 m

so the maximum height allowed is 20.4 m