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I'm trying to solve this problem and it's driving me a little crazy. Any help greatly appreciated.

Q) A lift travels to the top of a tower through a vertical displacement of 48 m. The total journey takes 17 s. The lift accelerates from rest at a constant rate for the first 5 seconds. Then it moves at constant speed and then decelerates to rest at a constant rate for the last 5 seconds.

What rate does the lift accelerate during the first 5 seconds?

My Attempt:

I have the initial and final velocity which are both zero (elevator starts and stops), displacement (48m) and time (overall time 17sec and three time intervals of acceleration, constant velocity and deceleration). Clearly the acceleration and deceleration will be same rates as they occur during the same time intervals. However with the information I have I feel I'm unable to use the usual constant acceleration equations.

The average velocity is 48/17 = 2.8 m/s. However I'm not sure how that helps.

To find the acceleration during the first 5 seconds, I have the time and initial velocity but I need the velocity

it reaches at 5 seconds to obtain the acceleration and I just can't work out how to get it.