A rollercoaster speeds up from rest to (45m/s) in 1.2s (37.5 m/s²). The roller coaster car then travels vertically upwards and decelerates at 10m/s² How much time passes before it is stationary (for a moment) ?

consider the motion of roller coaster in upward direction

v₀ = initial velocity as it starts travelling vertically upward = 45 rad/s

v = final velocity when it becomes stationary for a moment = 0 m/s

a = acceleration of roller coaster in upward direction = - 10 m/s²

t = time passed before the roller coaster becomes stationary

using the kinematics equation

v = v₀ + at

inserting the values

0 = 45 + ( - 10) t

0 - 45 = ( - 10) t

t = - 45 / ( - 10)

t = 4.5 sec