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# mechanics SUVAT help please watch

1. I know this is my maths course that Im studying (mechanics) but I feel this question is more apt for the physics section:

I have this question, but cannot rearrange any of the SUVAT equations to get the answer:

A set of traffic lights covers road repairs on a road. The traffic lights are 80m apart. Assume a car accelerates at 2ms^2 from rest until reaching a speed of 10ms^1 and then travels at a constant speed. What is the least time taken for a car starting from rest at the first set of lights to reach the next set?

****************

S= 80m
U= 0ms^1
V= 10ms^1
A= 2ms^2
T= ?

The answer is 10.5 seconds, the closest I have got is 8.9 seconds by rearranging s= ut + 1/2at^2 into the form of the quadratic formula.

thanks
2. You need to do this in three steps, splitting the motion into two parts
1. Use a formula to find how far the car went (s) from rest in the 1st part. (accelerating from 0 to 10 m/s)
You know a, u, and v.
2. Find t, the time taken using a different equation.
3. In the second part, find how long the car took to travel the rest of the 80m (80-s) at constant speed of 10m/s.
3. Split into 2 parts, the first while the car accelerates.
V=U+at, V=10, U=0, A=2. T=(V-U)/A= 5 seconds
s=ut+0.5at^2=0+0.5x2x5^2=25m
The car has now reached a steady velocity of 10ms^-1, and has travelled 25m. so to travel the last 55...
t=distance/speed=55/10=5.5seconds
SO
5 seconds accelerating+ 5.5 at constant velocity=10.5

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